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) = 3/2.Final value of log: The value of log_(4)8 is therefore 3/2. This is the exponent that 4 (which is 2^2) must be raised to in order to get 8.

Grade 8

Relationship between squares and square roots

Full solution

\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 $8$ .