What is the answer to log_{x}(4)=4 ?

The answer to log_{x}(4)=4 is x=sqrt(2)

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log_{x}(4)=4

lo g_{x} (4) = 4

x = 2

Decimal Notation

x = 1.41421 \dots

Solution steps

lo g_{x} (4) = 4

Apply log rules

\frac{1}{lo g _{4} ( x )} = 4

Multiply both sides by

lo g_{4} (x)

\frac{1}{lo g _{4} ( x )} lo g_{4} (x) = 4 lo g_{4} (x)

Simplify

1 = 4 lo g_{4} (x)

Switch sides

4 lo g_{4} (x) = 1

Divide both sides by

4

lo g_{4} (x) = \frac{1}{4}

Apply log rules

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

lo g_{x} (4) = 3

lo g_{x} (4) = 8

lo g_{10} (x) = 1.0992

8 (ln (2 x) + 1) = 0

lo g_{5} (x + 18) - lo g_{5} (x - 6) = 2