Question

Find the value of x :


log₁₀( 2ˣ + x - 41 ) = x ( 1 - log₁₀5 )


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Chapter : Logarithms


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Answer 1

Answer:

$log_{10}(2^x+x-41)=x-xlog_{10}5\\\\\implies log_{10}(2^x+x-41)=xlog_{10}10-log_{10}5^x\\\\\implies log_{10}(2^x+x-41)=log_{10}10^x-log_{10}5^x\\\\\implies log_{10}(2^x+x-41)=log_{10}\dfrac{10^x}{5^x}\\\\\implies 2^x+x-41=\dfrac{2^x\times 5^x}{5^x}\\\\\implies 2^x+x-41=2^x\\\\\implies x-41=0\implies x=41$

Step-by-step explanation:

$log_aa=1$

$alog_{b}c=log_bc^a$

$log_xa-log_xb=log_x\dfrac{a}{b}$