Test Index

Logarithms

© examsnet.com

Question : 39 of 85

Marks: +1, -0

If

\log_{3} x \log_{y} 3 \log_{2} y=5,

x

equals

$y^{5}$
243
32
none

Solution:

Concept:

Use logarithmic change of base to simplify the product into a single logarithm.

Explanation:

We have

\log_3 x \cdot \log_y 3 \cdot \log_2 y = 5

.

Rewrite

\log_y 3 = \frac{1}{\log_3 y}

and

\log_2 y = \frac{\log_3 y}{\log_3 2}

.

Substitute:

\log_3 x \cdot \frac{1}{\log_3 y} \cdot \frac{\log_3 y}{\log_3 2} = \frac{\log_3 x}{\log_3 2} = \log_2 x

.

Thus

\log_2 x = 5

, so

x = 2^5 = 32

.

Answer:

x = 32

© examsnet.com

Go to Question:

Prev Question

Next Question