What is the answer to log_{x}(216)=3 ?

The answer to log_{x}(216)=3 is x=6

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log_{x}(216)=3

lo g_{x} (216) = 3

x = 6

Solution steps

lo g_{x} (216) = 3

Apply log rules

\frac{1}{lo g _{216} ( x )} = 3

Multiply both sides by

lo g_{216} (x)

\frac{1}{lo g _{216} ( x )} lo g_{216} (x) = 3 lo g_{216} (x)

Simplify

1 = 3 lo g_{216} (x)

Switch sides

3 lo g_{216} (x) = 1

Divide both sides by

3

lo g_{216} (x) = \frac{1}{3}

Apply log rules

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

lo g_{7} (2 x - 1) = 2

6 lo g_{4} (x + 19) = 12

lo g_{2} (x^{2} - x - 1) = 2

lo g_{2} (2 x) = 2 lo g_{4} (x + 4)

lo g_{5} (2 x + 4) = 2