Logarithm Questions with Solutions

15 questions3 easy8 medium4 hard

A logarithm answers the question: to what power must a base be raised to give a number? If a^x = N, then log base a of N = x. This topic covers the laws of logarithms (product, quotient and power rules), change of base, common and natural logarithms, and solving logarithmic and exponential equations. Most exam questions reduce to applying the three main rules correctly: log(mn) = log m + log n, log(m/n) = log m - log n, and log(m^k) = k log m. Remember that logarithms are only defined for positive numbers and a base that is positive and not equal to 1, which helps you reject invalid answers. Practise the logarithm questions below. Each comes with a step-by-step solution showing which law is applied at each step.

All Questions Easy Medium Hard

Q1.
Find the value of $x$ , if $(2^{\frac{1}{l o g _{x} 4}}) (2^{\frac{1}{l o g _{x} 16}}) (2^{\frac{1}{l o g _{x} 256}}) \dots = 2$ .
A. $2$ B. $\frac{1}{2}$ C. $4$ D. $\frac{1}{4}$
hardAsked in NIMCET 2009View solution ›
Q2.
For $a > 0, a \neq = 1$ , the number of values of $x$ satisfying $2 l o g_{x} a + l o g_{a x} a + 3 l o g_{a^{2} x} a = 0$ is
A. $2$ B. $3$ C. $4$ D. $5$
hardAsked in NIMCET 2008View solution ›
Q3.
If $l o g (1 - x + x^{2}) = a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots$ , then $a_{3} + a_{6} + a_{9} + \dots$ is equal to
A. $l o g 2$ B. $\frac{2}{3} l o g 2$ C. $\frac{1}{3} l o g 2$ D. $2 l o g 2$
hardAsked in NIMCET 2021View solution ›
Q4.
If $(x_{0}, y_{0})$ is the solution of the equations $(2 x)^{l n 2} = (3 y)^{l n 3}$ and $3^{l n x} = 2^{l n y}$ , then $x_{0}$ is:
A. 1/6B. 1/3C. 1/2D. 6
hardAsked in NIMCET 2014View solution ›