If {log _{10}}3 = 0.477,the number of digits | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $y = 3^{40}$.Taking $\log_{10}$ on both sides,we get $\log_{10} y = \log_{10} (3^{40})$.Using the property $\log(a^b) = b \log a$,we have $\lo

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) Let $y = 3^{40}$.Taking $\log_{10}$ on both sides,we get $\log_{10} y = \log_{10} (3^{40})$.Using the property $\log(a^b) = b \log a$,we have $\log_{10} y = 40 	imes \log_{10} 3$.Given $\log_{10} 3 = 0.477$,so $\log_{10} y = 40 	imes 0.477 = 19.08$.The number of digits in $3^{40}$ is given by $\lfloor \log_{10} y floor + 1$.Here,$\lfloor 19.08 floor + 1 = 19 + 1 = 20$.Therefore,the number of digits is $20$.

If ${\log _{10}}3 = 0.477$,the number of digits in ${3^{40}}$ is

Similar Questions

For what values of $x$ is the following identity valid and holds? $\tanh^{-1}(x) = \frac{1}{2} \log_e \left( \frac{1+x}{1-x} \right)$.

If $\frac{1}{2} \le \log_{0.1} x \le 2$,then:

If $x = \log_{0.1} 0.001$ and $y = \log_9 81$,then $\sqrt{x - 2\sqrt{y}}$ is equal to

If $x = \log_3 5$ and $y = \log_{17} 25$,then which of the following is correct?

The number of solutions of the equation $\log _{(x+1)}(2 x^{2}+7 x+5)+\log _{(2 x+5)}(x+1)^{2}-4=0$ for $x > 0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module