Question

Find the logarithm of 2025 to the base 3√5

Answer 1

Given,

The information about logarithm is = logarithm of 2025 to the base 3√5

To find,

The final result of the given logarithmic expression.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the final result = x

According to the logarithmic process,

log₃√₅ (2025) = x

This implies

(3√5)ˣ = 2025 [Exponential form]

(3√5)ˣ = (3√5)⁴

x = 4

(This will be our final value of the given logarithmic expression.)

Hence, the final result is 4

Answer 2

SOLUTION

TO DETERMINE

The value of

$\sf{ log_{3 \sqrt{5} }(2025) }$

EVALUATION

$\sf{ log_{3 \sqrt{5} }(2025) }$

$\sf{ = log_{3 \sqrt{5} }(3 \times 3 \times 3 \times 3 \times 5 \times 5) }$

$\sf{ = log_{3 \sqrt{5} }( {3}^{4} \times {5}^{2} ) }$

$\sf{ = log_{3 \sqrt{5} } \bigg( {3}^{4} \times {( \sqrt{5}) }^{4} \bigg) }$

$\sf{ = log_{3 \sqrt{5} } \bigg(( {3 \sqrt{5}) }^{4}\bigg) }$

$\sf{ = 4 \times log_{3 \sqrt{5} } ( {3 \sqrt{5}) }}$

$\sf{ = 4 \times 1}$

$\sf{ = 4 }$

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