Alg9.4.21

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Simplify $log_{3\sqrt{2}}(5832)\,$

Let

$log_{3\sqrt{2}}(5832)=x\,$

Hence by using the formula,

$(3\sqrt{2})^x=5832\,$

Now expressing 5832 in terms of base value,

We get

$(3\sqrt{2})^x=729\cdot8\,$

$(3\sqrt{2})^x=3^6\cdot2^3\,$

Again it can be expressed as

$(3\sqrt{2})^x=(3\sqrt{2})^6)\,$

Comparing the indices on both sides

We get x=6,the answer for the given log is 6.

Main Page:Algebra:Logarithmic

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