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Chapter 5: Q 3. (page 308)

$a^{\log_{a} M}$

Short Answer

Expert verified

The value is M.

Step by step solution

01

Step 1. Given information.

Consider the given information.

$a^{\log_{a} M}$

02

Step 2. Calculation.

Rewrite the expression.

$y = a^{\log_{a} M}$

Take the log from both sides and apply the logarithm properties.

$\begin{array}{rcl} y & = & a^{\log_{a} M} \\ \log y & = & \log a^{\log_{a} M} \\ \log y & = & \log_{a} M \log a \\ \log y & = & \frac{\log M}{\log a} \cdot \log a \\ \log y & = & \log M \\ y & = & M \end{array}$

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