What is the answer to log_{x}(9)=4 ?

The answer to log_{x}(9)=4 is x=sqrt(3)

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log_{x}(9)=4

lo g_{x} (9) = 4

x = 3

Decimal Notation

x = 1.73205 \dots

Solution steps

lo g_{x} (9) = 4

Apply log rules

\frac{1}{lo g _{9} ( x )} = 4

Multiply both sides by

lo g_{9} (x)

\frac{1}{lo g _{9} ( x )} lo g_{9} (x) = 4 lo g_{9} (x)

Simplify

1 = 4 lo g_{9} (x)

Switch sides

4 lo g_{9} (x) = 1

Divide both sides by

4

lo g_{9} (x) = \frac{1}{4}

Apply log rules

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{10} (x) = 5.45

lo g_{2} (n) = 1 \cdot 1 0^{6}

lo g_{10} (3 x + 2) = 2

1.2 = lo g_{10} (x)

ln (x - 8) = 7