[tex]500=20(1.5)^{4x}\implies \cfrac{500}{20}=1.5^{4x}\implies 25=1.5^{4x}
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\textit{now, we'll take a common log, any will do, we'll use ln()}
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ln(25)=ln\left(1.5^{4x} \right)\\\\
-----------------------------\\\\
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\
-----------------------------\\\\
thus\implies ln(25)=4xln(1.5)\implies \cfrac{ln(25)}{4ln(1.5)}=x[/tex]
