What is the answer to log_{2x}(27)=3 ?

The answer to log_{2x}(27)=3 is x= 3/2

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log_{2x}(27)=3

lo g_{2 x} (27) = 3

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

lo g_{2 x} (27) = 3

Apply log rules

\frac{1}{lo g _{27} ( 2 x )} = 3

Multiply both sides by

lo g_{27} (2 x)

\frac{1}{lo g _{27} ( 2 x )} lo g_{27} (2 x) = 3 lo g_{27} (2 x)

Simplify

1 = 3 lo g_{27} (2 x)

Switch sides

3 lo g_{27} (2 x) = 1

Divide both sides by

3

lo g_{27} (2 x) = \frac{1}{3}

Apply log rules

2 x = 3

Solve

2 x = 3 : x = \frac{3}{2}

x = \frac{3}{2}

Verify Solutions:

x = \frac{3}{2}

True

The solution is

x = \frac{3}{2}

lo g_{x} (9) = \frac{3}{2}

ln (x) = ln (x + 1) - ln (2)

50 = 7.3718 ln (x) + 32.666

\frac{9}{5 ln ( x ^{2} - 3 )} = 4

lo g_{7} (x - 5) + lo g_{7} (3 x - 1) = 2