Question

find x
6^3x-5 = 1/36^x ​

Answer 1

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Answer 2

$\sf{6^{3x-5}=\dfrac{1}{36^x}}$

$\implies\sf{6^{3x-5}=36^{-x}}$

$\implies\sf{6^{3x-5}=\left(6^2\right)^{-x}}$

$\implies\sf{6^{3x-5}=6^{2\left(-x\right)}}$

$\bf{\bf{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\bf{,\:then\:}f\left(x\right)=g\left(x\right)}$

$\implies\sf{3x-5=2\left(-x\right)}$

$\implies\sf{3x-5=-2x}$

$\implies\sf{3x-5+5=-2x+5}$

$\implies\sf{3x=-2x+5}$

$\implies\sf{3x+2x=-2x+5+2x}$

$\implies\sf{5x=5}$

$\implies\bf{x=1}$