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Logarithms Practice Test 1

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Question : 18 of 40

Marks: +1, -0

\log_{179}\left(\frac{179}{\sqrt{32,041}}\right)

is equal to:

0
1
179
$\sqrt{179}$
None of these

Solution: 👈: Video Solution

Concept:

Simplify the argument of the logarithm, then use

\log_a(1)=0

.

Explanation:

First find

\sqrt{32,041}

.

Check whether

179

is its square root:

179^2=(180-1)^2=32400-360+1=32,041

.

So

\sqrt{32,041}=179

.

Now substitute this into the given expression:

\log_{179}\left(\frac{179}{\sqrt{32,041}}\right)=\log_{179}\left(\frac{179}{179}\right)

.

Simplify the fraction:

\frac{179}{179}=1

.

Thus the expression becomes

\log_{179}(1)

.

For any positive base

a\neq1

,

\log_a(1)=0

.

Therefore,

\log_{179}(1)=0

.

Answer:

0

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