Test Index

Logarithms Practice Test 1

© examsnet.com

Question : 10 of 40

Marks: +1, -0

\log_{2\sqrt{2}} 512 = ?

4
5
6
7

Solution: 👈: Video Solution

Concept:

Convert both numbers into powers of the same base, then use the logarithm power rule.

Explanation:

Write the base:

2\sqrt{2}=2\cdot 2^{1/2}=2^{3/2}

.

Write the argument:

512=2^9

.

Use the rule

\log_{a^m} a^n=\dfrac{n}{m}

.

So,

\log_{2^{3/2}}2^9=\dfrac{9}{3/2}

.

Simplify:

\dfrac{9}{3/2}=9\cdot\dfrac{2}{3}=6

.

Answer:

The value is

6

.

© examsnet.com

Go to Question:

Prev Question

Next Question