Prove That

Log₃8

Log₉16 Log₄10

= 3Log₁₀2

Solution

Problems: Logarithms

Find the logarithm of 19683 to the base 3√3

The cost of a machine is $100,000 and its effective life is 12 years. If the scrap realizes only $5,000, what amount should be retained out of profits at the end of each year to...

A man borrows $ 750 from a money-lender and the bill renewed after every half year at an increase of 21%. What time is elapse before it reaches $7,500?

A man aged 40 wishes his dependents to have $40,000 at his death. A banker agrees to pay this amount to his dependents on condition that the man makes equal annual payments of $ x...

A man buys a car of $ 16,000. He estimates that its value will depreciate each year by 20 per cent of its value at the beginning of the year. Find the depreciated value of...

Problem 69: Logarithm

A machine costs a company $52,000 and its effective life is estimated to be 25 years. A sinking fund...

On his 48th birthday a man decides to make a gift of $5,000 to a hospital. He decides to save the amount by making equal annual payments up to and including hi 60th birthday to...

A loan of $1000 is to be paid in 5 equal annual payments interest being at 6 per cent per annum compound interest and first payment being made after a year, Analyze the payment into...

A machine costs the company $97,000 and its effective life is estimated to be 12 years. If the scrap realizes $2,000 only, what amount should be retained out of profits at the end of each...

A man wishes to create an endowment fund to provide an annual prize of $500 out of its income. If the fund is invested in 2½% p.a., find the amount of this fund.

What sum should be paid for an annuity of $2,400 for 20 years at 4½% compound interest p.a.?

The annual subscription for the membership of a club is $25 and a person may become a life member by paying $1000 in a lump sum. Find the rate of interest charged.

A loan of $40,000 is to be repaid in equal annual installment consisting of principal and interest due in course of 30 years. Find the amount of each installment reckoning interest at 4% p.a.

A man borrows $1000 on the understanding that it is to be paid back in four equal installments at intervals of six months; the first payment to be made six months after the money was...

A company buys a machine for $100,000. Its estimated life is 12 years and scrap value is $5000. What amount is to be retained every year from the profit and allowed to accumulate at 5%...

A man borrows $1500 promising to repay the sum borrowed and the proper interest by 10 equal yearly installments, the first two falling due in 1 year’s time. Reckoning C.I. at 5% p.a., find the...

Find the amount and present value of an annuity certain of $150 for 12 years, reckoning interest at 3½% p.a.

Problem 57: Logarithm

A machine costs a company $65,000 and its effective life is estimated to be 25 years. A sinking fund...

A man borrows $6000 at 6% and promises to pay off the loan in 20 annual payments beginning at the end of the first year. What in the annual payment necessary?

Problem 55: Logarithm

Calculate the amount and present value of an annuity of $3000 for 15 years if the rate of interest b...

Problem 54: Logarithm

Find the present value of an annuity of $1000 p.a. for 14 years following compound interest at 5% p....

Problem 53: Logarithm

A machinery in a factory is valued at $49074 and it is decided to reduce the estimated value at the ...

Problem 52: Logarithm

A machine depreciates at the rate of 10% of its value at the beginning of a year. The machine was pu...

In what time will a sum of money treble itself at 5% p.a. compound interest payable half-yearly?

In what time will a sum of money double itself at 5% p.a., compound interest?

A owes B $1600 but it is not due for payment till the end of 3 years from this date. How much should A pay B if he is willing to accept now in order...

Problem 48: Logarithm

A man left $18000 with the direction that it should be divided in such a way that his 3 sons aged 9,...

Find the compound interest on $25800 for 5 years if the rate of interest be 2% in the 1st year, 2½% in the second year, 3% in the 2rd year and thereafter at 4% p.a....

What is the present value of $1000 due in 2 years at 5% p.a. compound interest, according as the interest is paid (a) yearly or (b) half yearly?

Find the compound interest on $6950 for 3 years, if interest is payable half yearly, the rate for the first two years being 6%, and for the third year 9% p.a.

Find the difference between simple and compound interest on $5000 invested for 4 years at 5% per annum, interest payable yearly.

(a) Find the compound interest on $1000 for 4 years at 5% per annum. (b) What will be the simple interest in the above case?

A man wishes to create an endowment fund to provide an annual prize of $500. If the fund is invested at 10% p.a. C.I., find the amount of this fund.

A machine costs the company $97,000 and its effective life is estimated to be 12 years. If the scrap realizes $2,000 only, what amount should be retained out of profits at the end of each...

A limited company intends to create a depreciation fund to replace at the end of his 25th year assets costing $100,000. Calculate the amount to be retained out of profits every year if the interest...

A sinking fund is created for the redemption of debentures of $100,000/- at the end of 25 years. How much money should be provided out of profits each year for the sinking fund if the...

A man retires at the age of 60 years and his employer gives him a pension of Rs. 1,200 a year paid in half-yearly installments for the rest of his life. Reckoning his expectation of...

A wagon is purchased on installment basis, such that Rs. 5000 is to be paid on the signing of the contract and four yearly installments of Rs. 3000 each payable at the end of the...

A man borrows Rs. 20,000 at 4% C.I. and agrees to pay both the principal and the interest in 10 equal annual installments at the end of each year, find the amount of these installments....

A machine is depreciated in such a way that the value of the machine at the end of any year is 90% of the value at the beginning of the year. The cost of the...

A machine, the life of which is estimate to be 10 years, costs Rs. 10,000. Calculate its scrap value at the end of its life, depreciation on the reducing installment system being charged at 10%...

Find the logarithm of 784 to the base 2√7

(a) Find the number of years and the fraction of a year in which a sum of money will treble itself at compound interest at 8 per cent per annum. (b) In what time will...

Mr. Mehta borrowed Rs. 20,000 from a money-lender but he could not repay any amount in a period of 4 years. Accordingly the money-lender demands now Rs. 26,500 from him. At what rate per cent...

What is the present value of Rs. 10,000 due in 2 years at 8% p.a., C.I. according as the interest is paid (a) yearly or (b) half-yearly?

Find the compound interest on Rs. 6950 for 3 years if interest is payable half yearly, the rate for the first two years being 6% p.a., and for the third year 9% p.a.

Find the component interest of Rs. 10,000 for 4 years at 5% per annum. What will be the simple interest in the above case?

Logarithms

Prove That

Solution

Problems: Logarithms

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