What is the answer to log_{2x}(81)= 4/3 ?

The answer to log_{2x}(81)= 4/3 is x= 27/2

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log_{2x}(81)= 4/3

lo g_{2 x} (81) = \frac{4}{3}

x = \frac{27}{2}

Decimal Notation

x = 13.5

Solution steps

lo g_{2 x} (81) = \frac{4}{3}

Apply log rules

\frac{1}{lo g _{81} ( 2 x )} = \frac{4}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 3 = lo g_{81} (2 x) \cdot 4

Simplify

3 = lo g_{81} (2 x) \cdot 4

Switch sides

lo g_{81} (2 x) \cdot 4 = 3

Divide both sides by

4

lo g_{81} (2 x) = \frac{3}{4}

Apply log rules

2 x = 27

Solve

2 x = 27 : x = \frac{27}{2}

x = \frac{27}{2}

Verify Solutions:

x = \frac{27}{2}

True

The solution is

x = \frac{27}{2}

lo g_{10} (x) = - 4.67

lo g_{10} (x) - lo g_{10} (x - 1) = 1

ln (x + 4) = 1

lo g_{6} (8 x) - 3 lo g_{6} (3) = 0

lo g_{6} (x^{2}) = 4

What is the answer to log_{2x}(81)= 4/3 ?
The answer to log_{2x}(81)= 4/3 is x= 27/2
Solve for x: log_{2x}(81)= 4/3
The solution is x= 27/2