Question

how many digits are there in 12550 given that log 5= 0.69897?

Answer 1

Answer:

Correct answer is 6 digits in 0.69897

Answer 2

Concept

Logarithmic functions are given as the inverses of exponential functions. Any exponential expression can be rewritten in the form of a logarithmic equation.

Given

log 5= 0.69897

Find

Number of digits in $125^{50}$.

Solution

Let us take $125^{50} = x$

Taking logarithms to the base 10 on both sides we get,

$log125^{50} = logx$ ....... (1)

By property of logarithms,

$log(m)^n=nlog(m)$

125 can be rewritten as;

$125 = 5^3$

Thus, solving (1), we get,

$logx = log125^{50}\\ logx = 50.\ log 125\\logx = 50.\ log (5^3)\\logx = 50.\ 3.\ log 5\\logx = 50.\ 3.\ 0.69897\\logx = 104.8455$

Now,

For $log10$, the mantissa is 1.

For $log100$, the mantissa is 2.

So, the number of digits = 1 + mantissa of that number of logarithm to the base 10.

Therefore the number of digits in $x = 1 + 104$.

But $x=125 ^{50}$

Hence, the number of digits in $125 ^{50}$ are 105.