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log_(4)8=

$\log _{4} 8=$

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Relationship between squares and square roots

Full solution

Q.

\log _{4} 8=

Find value of $\log$ : We need to find the value of $\log_{4}8$ . This means we are looking for the exponent that $4$ must be raised to in order to get $8$ .
Express $8$ and $4$ as powers of $2$ : We can express $8$ as $2^3$ and $4$ as $2^2$ . This will allow us to use the property of logarithms that states $\log_{b}(b^x) = x$ .
Rewrite expression with new representations: Rewrite the original expression using the new representations of $8$ and $4$ : $\log_{(2^2)}(2^3)$ .
Apply property of logarithms: Apply the property of logarithms that allows us to divide the exponents when the base of the logarithm and the argument have the same base: $\log_{2^2}(2^3) = \frac{3}{2}$ .
Final value of log: The value of $\log_{4}8$ is therefore $\frac{3}{2}$ . This is the exponent that $4$ (which is $2^{2}$ ) must be raised to in order to get $8$ .

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