# Determine the algebraic modeling Solve for x: displaystyle{32}{left({1.05}right)}^{x}={90}

Determine the algebraic modeling
Solve for x: $32{\left(1.05\right)}^{x}=90$
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Tuthornt
Given: $32{\left(1.05\right)}^{x}=90$
Used concept:
$\mathrm{log}{a}^{b}=b\mathrm{log}a$
On solving the given equation,
$32{\left(1.05\right)}^{x}=90$
${\left(1.05\right)}^{x}=\frac{90}{32}$
On taking logarithm both sides, to obtain
$\mathrm{log}{\left(1.05\right)}^{x}=\mathrm{log}\left(\frac{90}{32}\right)$
$x\mathrm{log}\left(1.05\right)=\mathrm{log}\left(2.8125\right)$
$x=\frac{\mathrm{log}\left(2.8125\right)}{\mathrm{log}\left(1.05\right)}$
$x\approx 21.194$