Solveeit Logo
Login

Question

Question: If log<sub>3</sub>x = a and log<sub>7</sub>x = b, then which of the following is equal otlog<sub>21<...

If log3x = a and log7x = b, then which of the following is equal otlog21x?

A

ab

B

aba–1+b–1\frac{ab}{a^{–1} + b^{–1}}

C

1a+b\frac{1}{a + b}

D

1a–1+b–1\frac{1}{a^{–1} + b^{–1}}

Answer

1a–1+b–1\frac{1}{a^{–1} + b^{–1}}

Explanation

Solution

\ log3x = a ̃ 1/a = logx3 & log7x = b ̃ 1/b = logx7

\log21x=1log⁡x21\frac{1}{\log_{x}21}=1log⁡x3+log⁡x7\frac{1}{\log_{x}3 + \log_{x}7}=11/a+1/b\frac{1}{1/a + 1/b}