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

The answer to log_{3}(4^x)=1-2x is x=(ln(3))/(2ln(6))

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

The solution is x=(ln(3))/(2ln(6))

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

x = \frac{ln ( 3 )}{2 ln ( 6 )}

Decimal Notation

x = 0.30657 \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{ln ( 3 )}{2 ln ( 6 )}

x = \frac{ln ( 3 )}{2 ln ( 6 )}

Verify Solutions:

x = \frac{ln ( 3 )}{2 ln ( 6 )}

True

The solution is

x = \frac{ln ( 3 )}{2 ln ( 6 )}

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

2 ln (x) = ln (x^{2})

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

ln (- 4 - x) + ln (3) = ln (2 - x)

- 3 lo g_{2} (5 x) = - 12

What is the answer to log_{3}(4^x)=1-2x ?
The answer to log_{3}(4^x)=1-2x is x=(ln(3))/(2ln(6))
Solve for x: log_{3}(4^x)=1-2x
The solution is x=(ln(3))/(2ln(6))