If ₓ y = 100 and ₂x = 10, then find the value of y.

Correct Answer is : 210002¹000}21000

Correct Answer is : 210002¹000}21000

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Logarithms Practice Test 1

Question : 11 of 40

Marks: +1, -0

\log_x y = 100

\log_{2}x = 10

, then find the value of y.

Solution: 👈: Video Solution

Concept:

A logarithm can be rewritten in exponential form: if

\log_a b=c

, then

b=a^c

Explanation:

Given

\log_2 x=10

, convert to exponential form:

x=2^{10}

Given

\log_x y=100

, convert to exponential form:

y=x^{100}

Substitute

x=2^{10}

into

y=x^{100}

y=(2^{10})^{100}

Apply the power rule

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

y=2^{10 \times 100}=2^{1000}

So the value of

y

2^{1000}

, which matches option B.

Answer:

y=2^{1000}

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