How do you solve $12^{x} = 14^{3 x}$ $12^x=14^(3x)$ ?

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How do you solve $12^{x} = 14^{3 x}$ $12^x=14^(3x)$ ?

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Answer 1 · 2015-08-05T13:05:44

I found: $x = 0$ $x=0$

Explanation:

Take the natural log (ln) on both sides:
${ln 12}^{x} = {ln 14}^{3 x}$ $ln12^x=ln14^(3x)$
use the property that:
${ln x}^{a} = a ln x$ $lnx^a=alnx$ to get:
$x ln 12 = 3 x ln 14$ $xln12=3xln14$
$x ln 12 - 3 x ln 14 = 0$ $xln12-3xln14=0$
so:
$x (ln 12 - 3 ln 14) = 0$ $x(ln12-3ln14)=0$

this is true only if $x = 0$ $x=0$

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How do you solve $12^{x} = 14^{3 x}$ $12^x=14^(3x)$ ?

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