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Logarithms

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Question : 6 of 85

Marks: +1, -0

If

\log_{10}[\log_{10}(\log_{10} x)]=0

then the value of

x

is

1
10
$10^{10}$
100

Solution:

Concept:

Use the property

\log_a b = c \implies b = a^c

repeatedly from the outermost logarithm inward.

Explanation:

We start with

\log_{10}[\log_{10}(\log_{10} x)] = 0

.

Since

\log_{10} (\text{anything}) = 0

means the argument is

10^0 = 1

, we get:

\log_{10}(\log_{10} x) = 1

.

Now

\log_{10}(\log_{10} x) = 1

implies

\log_{10} x = 10^1 = 10

.

Finally,

\log_{10} x = 10

implies

x = 10^{10}

.

Answer:

x = 10^{10}

, which corresponds to option C.

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