What is the answer to log_{x}(1728)=3 ?

The answer to log_{x}(1728)=3 is x=12

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log_{x}(1728)=3

lo g_{x} (1728) = 3

x = 12

Solution steps

lo g_{x} (1728) = 3

Apply log rules

\frac{1}{lo g _{1728} ( x )} = 3

Multiply both sides by

lo g_{1728} (x)

\frac{1}{lo g _{1728} ( x )} lo g_{1728} (x) = 3 lo g_{1728} (x)

Simplify

1 = 3 lo g_{1728} (x)

Switch sides

3 lo g_{1728} (x) = 1

Divide both sides by

3

lo g_{1728} (x) = \frac{1}{3}

Apply log rules

x = 12

Verify Solutions:

x = 12

True

The solution is

x = 12

y, x = ln ∣ y ∣

lo g_{3} (lo g_{8} (x)) = 1

lo g_{a} (27) = 3

2 x + ln (x) = 0

w, 0 = 20 lo g_{10} (w)