Question

Cly cloudy

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Solve for x, rounding to the nearest hundredth.
110 • 10^4x = 55

Answer 1

`110\cdot 10^(4x)=55\implies 10^(4x)=\cfrac{55}{110}\implies 10^(4x)=\cfrac{1}{2}\implies 10^(4x)=2^(-1) \\\\\\ \log\left( 10^(4x) \right)=\log\left( 2^(-1) \right)\implies 4x\log_(10)\left( 10 \right)=-1\log_(10)(2)\implies 4x(1)=-\log(2) \\\\\\ 4x=-\log(2)\implies x=-\cfrac{\log(2)}{4}\implies {\LARGE \begin{array}{llll} x\approx -0.08 \end{array}}`