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Oksi-84 [34.3K]
3 years ago
10

When and how do you use logarithms to solve exponential equations? give an example of an exponential equation that does not requ

ire logarithms to solve it and example of a problem that does require logarithms to solve it.
Mathematics
1 answer:
tatuchka [14]3 years ago
6 0
\bf 5^{x+3}=\cfrac{1}{125}\implies 5^{x+3}=\cfrac{1}{5^3}\implies 5^{x+3}=5^{-3}
\\\\\\
\textit{because the bases are the same, the exponents must also be the same}
\\\\\\
x+3=-3\implies \boxed{x=-6}\\\\
-------------------------------\\\\
3^x=4^{2x}\implies log(3^x)=log(4^{2x})\implies xlog(3)=(2x)log(4)
\\\\\\
\cfrac{x}{2x}=\cfrac{log(4)}{log(3)}\implies \cfrac{1}{x}=\cfrac{log(4)}{log(3)}\implies \cfrac{log(3)}{log(4)}=x\implies \boxed{0.79248125\approx x}
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