How do you solve $3^x=2^(x-1)$ ?

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Answer 1 · 2018-04-16T12:37:57

$color(blue)(x~~-1.709511290)$

$3^x=2^(x-1)$

Taking logarithms of both sides:

$xln(3)=(x-1)ln(2)$

$xln(3)=xln(2)-ln(2)$

$xln(3)-xln(2)=-ln(2)$

Factor:

$x(ln(3)-ln(2))=-ln(2)$

$x=(-ln(2))/(ln(3)-ln(2))~~-1.709511290$

$color(blue)(x~~-1.709511290)$

How do you solve 3^x=2^(x-1)3^x=2^(x-1)?