What is the answer to log_{4x}(x)= 9/5 ?

The answer to log_{4x}(x)= 9/5 is x= 1/(e^{\frac{9ln(2)){2}}}

Solve for x: log_{4x}(x)= 9/5

The solution is x= 1/(e^{\frac{9ln(2)){2}}}

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lo g_{4 x} (x) = \frac{9}{5}

x = \frac{1}{e ^{\frac{9 l n ( 2 )}{2}}}

Decimal

x = 0.04419 \dots

Solution steps

lo g_{4 x} (x) = \frac{9}{5}

Apply log rules

\frac{ln ( x )}{ln ( 4 x )} = \frac{9}{5}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

ln (x) \cdot 5 = ln (4 x) \cdot 9

Apply log rules

x = \frac{1}{e ^{\frac{9 l n ( 2 )}{2}}}

Verify Solutions:

x = \frac{1}{e ^{\frac{9 l n ( 2 )}{2}}}

True

The solution is

x = \frac{1}{e ^{\frac{9 l n ( 2 )}{2}}}

ln (x) + ln (4) = 2

lo g_{3} (x^{2} + 9) = 4

(2 lo g_{4} (x)) - (lo g_{4} (9)) = 2

ln (4 x + 1) = 6

lo g_{4} (1 - 2 x) = 2

What is the answer to log_{4x}(x)= 9/5 ?
The answer to log_{4x}(x)= 9/5 is x= 1/(e^{\frac{9ln(2)){2}}}
Solve for x: log_{4x}(x)= 9/5
The solution is x= 1/(e^{\frac{9ln(2)){2}}}