# Solve for x 1200(1.03)^x=800(1.08)^x

Solve for x $1200{\left(1.03\right)}^{x}=800{\left(1.08\right)}^{x}$
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Jozlyn
$1200\left({1.03}^{x}\right)=800\left({1.08}^{x}\right)$
divide by 800 on both sides
divide by ${1.03}^{x}$ on both sides
$\frac{1200}{800}=\frac{{1.08}^{x}}{{1.03}^{x}}$
$\frac{3}{2}={\left(\frac{1.08}{1.03}\right)}^{x}$
$\mathrm{ln}\left(\frac{3}{2}\right)=\mathrm{ln}\left({\left(\frac{1.08}{1.03}\right)}^{x}\right)$
$\mathrm{ln}\left(\frac{3}{2}\right)=x\cdot \mathrm{ln}\left(\frac{1.08}{1.03}\right)$
Exact: $x=\frac{\mathrm{ln}\left(\frac{3}{2}\right)}{\mathrm{ln}\left(\frac{1.08}{1.03}\right)}$
Decimal, approximate: x = about 8.554