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Solution assignment 09 Exponential equations

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Assignment 9

Solve:

(0.3)^{x-1}=5

Solution

The right-hand side does not contain a base 3 so we apply the logarithm at both sides:

(x-1)\log(0.3)=\log(5)

x-1=\displaystyle\frac{\log(5)}{\log(0.3)}=\displaystyle\frac{\log(5)}{\log(3)-\log(10)}=\displaystyle\frac{\log(5)}{\log(3)-1}

x=1+\displaystyle\frac{\log(5)}{\log(3)-1}

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