Question

What is the logarithmic form for mula1" title="2 { }^{x - 4} = 32" alt="2 { }^{x - 4} = 32" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$2^x-4=32\quad :\quad x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=5.16992\dots \right)\\\\2^x-4=32 \\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\2^x-4+4=32+4\\\mathrm{Simplify}\\2^x=36\\\\apply exponential rule\\x\ln \left(2\right)=\ln \left(36\right)\\x\ln \left(2\right)=\ln \left(36\right)\\x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}$

hope it helps:)