What is the answer to log_{3x}(18)=log_{4}(8) ?

The answer to log_{3x}(18)=log_{4}(8) is x=3^{1/3}*2^{2/3}

Solve for x: log_{3x}(18)=log_{4}(8)

The solution is x=3^{1/3}*2^{2/3}

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lo g_{3 x} (18) = lo g_{4} (8)

x = 3^{\frac{1}{3}} \cdot 2^{\frac{2}{3}}

Decimal Notation

x = 2.28942 \dots

Solution steps

lo g_{3 x} (18) = lo g_{4} (8)

Apply log rules

\frac{1}{lo g _{18} ( 3 x )} = \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{18} (3 x) \cdot 3

Simplify

2 = lo g_{18} (3 x) \cdot 3

Switch sides

lo g_{18} (3 x) \cdot 3 = 2

Divide both sides by

3

lo g_{18} (3 x) = \frac{2}{3}

Apply log rules

3 x = 1 8^{\frac{2}{3}}

Solve

3 x = 1 8^{\frac{2}{3}} : x = 3^{\frac{1}{3}} \cdot 2^{\frac{2}{3}}

x = 3^{\frac{1}{3}} \cdot 2^{\frac{2}{3}}

Verify Solutions:

x = 3^{\frac{1}{3}} \cdot 2^{\frac{2}{3}}

True

The solution is

x = 3^{\frac{1}{3}} \cdot 2^{\frac{2}{3}}

lo g_{x} (8) = 3

ln (7 + 2 x) = ln (1 + 4 x)

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

lo g_{10} (5 x) + lo g_{10} (x + 5) = 1

ln (9 x + e) = 7

What is the answer to log_{3x}(18)=log_{4}(8) ?
The answer to log_{3x}(18)=log_{4}(8) is x=3^{1/3}*2^{2/3}
Solve for x: log_{3x}(18)=log_{4}(8)
The solution is x=3^{1/3}*2^{2/3}