Question

If the logarithm of 324 to base a is 4, then find a

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The value of a = 3√2

Given :

The logarithm of 324 to base a is 4

To find :

The value of a

Solution :

Step 1 of 2 :

Form the equation

Here it is given that logarithm of 324 to base a is 4

By the given condition

$\displaystyle \sf{ log_{a}(324) = 4 }$

Step 2 of 2 :

The value of a

$\displaystyle \sf{ log_{a}(324) = 4 }$

$\displaystyle \sf{ \implies {a}^{4} = 324 }$

$\displaystyle \sf{ \implies {a}^{4} = 3 \times 3 \times 3 \times 3 \times 2 \times 2 }$

$\displaystyle \sf{ \implies {a}^{4} = {3}^{4} \times {2}^{2} }$

$\displaystyle \sf{ \implies {a}^{4} = {(3 \sqrt{2} )}^{4} }$

$\displaystyle \sf{ \implies a = 3 \sqrt{2} }$

Hence the required value of a = 3√2

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