What is the answer to log_{4x}(3x)= 3/7 ?

The answer to log_{4x}(3x)= 3/7 is x=e^{(6ln(2)-7ln(3))/4}

Solve for x: log_{4x}(3x)= 3/7

The solution is x=e^{(6ln(2)-7ln(3))/4}

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lo g_{4 x} (3 x) = \frac{3}{7}

x = e^{\frac{6 l n ( 2 ) - 7 l n ( 3 )}{4}}

Decimal

x = 0.41360 \dots

Solution steps

lo g_{4 x} (3 x) = \frac{3}{7}

Apply log rules

\frac{ln ( 3 x )}{ln ( 4 x )} = \frac{3}{7}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (3 x) \cdot 7 = ln (4 x) \cdot 3

Apply log rules

x = e^{\frac{6 l n ( 2 ) - 7 l n ( 3 )}{4}}

Verify Solutions:

x = e^{\frac{6 l n ( 2 ) - 7 l n ( 3 )}{4}}

True

The solution is

x = e^{\frac{6 l n ( 2 ) - 7 l n ( 3 )}{4}}

lo g_{x} (\frac{1}{625}) = - 4

ln (2 x - 1) = - 3

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

lo g_{10} (x - 1) = 0

lo g_{3} (x^{2} - 5 x + 9) = 2

What is the answer to log_{4x}(3x)= 3/7 ?
The answer to log_{4x}(3x)= 3/7 is x=e^{(6ln(2)-7ln(3))/4}
Solve for x: log_{4x}(3x)= 3/7
The solution is x=e^{(6ln(2)-7ln(3))/4}