What is the answer to log_{4}(2^x)=5x+3 ?

The answer to log_{4}(2^x)=5x+3 is x=-2/3

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log_{4}(2^x)=5x+3

lo g_{4} (2^{x}) = 5 x + 3

x = - \frac{2}{3}

Decimal

x = - 0.66666 \dots

Solution steps

lo g_{4} (2^{x}) = 5 x + 3

f (x) = g (x),

then

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

4^{l o g_{4} (2^{x})} = 4^{5 x + 3}

Simplify

4^{l o g_{4} (2^{x})} : 2^{x}

2^{x} = 4^{5 x + 3}

Solve

2^{x} = 4^{5 x + 3} : x = - \frac{2}{3}

x = - \frac{2}{3}

Verify Solutions:

x = - \frac{2}{3}

True

The solution is

x = - \frac{2}{3}

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

ln (x + 1) - ln (x - 1) = \frac{1}{2}

8 lo g_{10} (10 x + 5) = 16

2 (4 x ln (x) + 2 x) = 0

lo g_{12} (x) + lo g_{12} (11 x - 1) = 1

What is the answer to log_{4}(2^x)=5x+3 ?
The answer to log_{4}(2^x)=5x+3 is x=-2/3
Solve for x: log_{4}(2^x)=5x+3
The solution is x=-2/3