What is the answer to 2log_{x}(12)=1 ?

The answer to 2log_{x}(12)=1 is x=144

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2log_{x}(12)=1

2 lo g_{x} (12) = 1

x = 144

Solution steps

2 lo g_{x} (12) = 1

Divide both sides by

2

lo g_{x} (12) = \frac{1}{2}

Apply log rules

\frac{1}{lo g _{12} ( x )} = \frac{1}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{12} (x) \cdot 1

Simplify

2 = lo g_{12} (x)

Apply log rules

144 = x

Switch sides

x = 144

Verify Solutions:

x = 144

True

The solution is

x = 144

2 ln (x + 1) = ln ((x + 1)^{22})

2 \cdot ln (x + 3) + 4 = x

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

ln (x^{2} + 1) + 1 = ln (x + 1)

lo g_{3} (6 x + 5) = 2