What is the answer to log_{3}(4x)=1-2x ?

The answer to log_{3}(4x)=1-2x is x=(\W_{0}((3ln(3))/2))/(2ln(3))

Solve for x: log_{3}(4x)=1-2x

The solution is x=(\W_{0}((3ln(3))/2))/(2ln(3))

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lo g_{3} (4 x) = 1 - 2 x

x = \frac{W _{0} ( \frac{3 l n ( 3 )}{2} )}{2 ln ( 3 )}

Decimal Notation

x = 0.34863 \dots

Solution steps

lo g_{3} (4 x) = 1 - 2 x

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

3^{l o g_{3} (4 x)} = 3^{1 - 2 x}

Simplify

3^{l o g_{3} (4 x)} : 4 x

4 x = 3^{1 - 2 x}

Solve

4 x = 3^{1 - 2 x} : x = \frac{W _{0} ( \frac{3 l n ( 3 )}{2} )}{2 ln ( 3 )}

x = \frac{W _{0} ( \frac{3 l n ( 3 )}{2} )}{2 ln ( 3 )}

Verify Solutions:

x = \frac{W _{0} ( \frac{3 l n ( 3 )}{2} )}{2 ln ( 3 )}

True

The solution is

x = \frac{W _{0} ( \frac{3 l n ( 3 )}{2} )}{2 ln ( 3 )}

lo g_{\frac{5}{2}} (x) = 3

ln (x) = ln (5) + ln (9)

lo g_{4} (5 x + 6) = 4

4 = \frac{ln ( 2 b )}{ln ( 4 b )}

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

What is the answer to log_{3}(4x)=1-2x ?
The answer to log_{3}(4x)=1-2x is x=(\W_{0}((3ln(3))/2))/(2ln(3))
Solve for x: log_{3}(4x)=1-2x
The solution is x=(\W_{0}((3ln(3))/2))/(2ln(3))