Logarithms Questions for CAT

Which of the following statements is incorrect?

Evaluate $\log_{100}(10)$.

Evaluate $\log_{10}(1000)$.

What value of $y$ satisfies the following equation? $\log_{10}(2y+y-41) = y(1-\log_{10} 5)$

Find the characteristic of $\log_{10}(450)$.

Compute the value of $\log_{2} 32$.

If $\log_{7} 4,\; \log_{7}\!\big(2^{x}-6\big),\; \log_{7}\!\big(2^{x}-7\big)$ are in arithmetic progression, then the value of $x$ is

Evaluate $\log_{7} (343 \sqrt{7})$.

What is the number of integers that satisfy: $2\log_4(x^2+2x+16) < 8$?

How many solutions does the equation $\log_9 |x-3| = \log_3 (x-5)$ have?

Determine how many integer values of $x$ satisfy: $\log_{0.33}(x^2 - 3x + 2) > \log_{0.33}(6)$

How many distinct integer values of n satisfy the inequality 4 − log₂ n − log₄ n < 0?

How many digits are in the number $60^{20}$ if $\log 2 = 0.3010$ and $\log 3 = 0.4771$?

If $\log_{10}(2)=0.3010$ and $\log_{10}(3)=0.4771$, find $\log_{10}(18)$.

If $\log_{2}\big[\log_{9}(t^{2}+5)\big]=2$, find the possible value(s) of $t$.

Given that log₁₂27 = a and log₉16 = b, what is log₈108?

Given that $3\log_2 M - 6 = \log_2 N$ and $2\log_3 N - 3 = \log_3 M$, how many factors does $M^5 N^5$ have?

If $\log_{3}\big[2+\log_{2}\{5+\log_{5}(x-2)\}\big]-1=0$, then find $125x$.

Given that $\log 2=0.3$ and $\log 3=0.47$, determine the number of digits in $36^{19}$ when expressed in base 15.

Find the number of distinct real solutions to the following equations, $2Y = 9 - \log_{2}{X}$ and $X^{Y} = 512$