Solution assignment 09 Logarithmic functions and graphs

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Assignment 9

Solve:

$5^x=4$

Solution

It is clear that $x>0$ ( $5^0=1$ ) and $x<1$ $(5^1=5)$ , but the more exact value is not possible to calculate without applying logarithms. We take the logarithm (any base will do, so we take $b=10$ ) of the left- and right-hand side:

$\log(5^x)=\log(4)$

$x\log(5)=\log(4)$

$x=\displaystyle\frac{\log(4)}{\log(5)}\approx0.86$

Return to Assignments Logarithmic functions and graphs

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Solution assignment 09 Logarithmic functions and graphs

Assignment 9

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