Question

the number of digits in 8^15 5^40

Answer 1

The answer is 42 digits..........

Answer 2

The number of digits in $8^{15}$ and $5^{40}$ is $14$ and $28$

Step-by-step explanation:

Given,

The number of digits in $8^{15}$ and $5^{40}$

Let,

$x=8^{15}$

Take log on both sides,

$log(x)=log(8^{15})$

⇒$log(x)=15log(8)$

⇒$log(x)=13.546$

Its indicates that $8^{15}$ has $(13+1)=14$ digits.

This can also be verified as under:

$log(x)=13.546$

⇒$x=10^{13.546}$

∴ $x=35156044052830$

∴ The number of digits in $8^{15}$ is $14$

Similarly,

$x=5^{40}$

Take log on both sides,

$log(x)=log(5^{40})$

⇒$log(x)=40log(5)$

⇒$log(x)=27.958$

Its indicates that $5^{40}$ has $(27+1)=28$ digits.

This can also be verified as under:

$log(x)=27.958$

⇒$x=10^{27.958}$

∴ $x= 9.078205301\times 10^{27}$

∴ The number of digits in $5^{40}$ is $28$