Test Index

Logarithms

© examsnet.com

Question : 5 of 85

Marks: +1, -0

If

\log_{100000} x = -\frac{1}{5}

then the value of

x

is

$\frac{1}{10000}$
$\frac{1}{1000}$
$\frac{1}{100}$
$\frac{1}{10}$

Solution:

Concept:

Use the definition of a logarithm:

\log_a b = c

implies

a^c = b

.

Explanation:

Given

\log_{100000} x = -\frac{1}{5}

.

Rewrite in exponential form:

x = (100000)^{-1/5}

.

Express

100000

as a power of

10

:

100000 = 10^5

.

So

x = (10^5)^{-1/5}

.

Apply the exponent rule

(a^m)^n = a^{mn}

:

x = 10^{5 \cdot (-\frac{1}{5})} = 10^{-1}

.

10^{-1} = \frac{1}{10}

.

Thus,

x = \frac{1}{10}

.

Answer:

D.

\frac{1}{10}

© examsnet.com

Go to Question:

Prev Question

Next Question