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

The answer to log_{4}(2^{3-5x})=x^2 is x= 1/2 ,x=-3

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

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

x = \frac{1}{2}, x = - 3

Decimal Notation

x = 0.5, x = - 3

Solution steps

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

f (x) = g (x),

then

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

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

Simplify

4^{l o g_{4} (2^{3 - 5 x})} : 2^{3 - 5 x}

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

Solve

2^{3 - 5 x} = 4^{x^{2}} : x = \frac{1}{2}, x = - 3

x = \frac{1}{2}, x = - 3

Verify Solutions:

x = \frac{1}{2}

True

, x = - 3

True

The solutions are

x = \frac{1}{2}, x = - 3

lo g_{10} (x + 8) + lo g_{10} (9) = 1

lo g_{10} (x) - lo g_{10} (x + 3) = - 1

x \cdot ln (x) = 0

ln (5 x + 1) + ln (x) = ln (4)

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

What is the answer to log_{4}(2^{3-5x})=x^2 ?
The answer to log_{4}(2^{3-5x})=x^2 is x= 1/2 ,x=-3
Solve for x: log_{4}(2^{3-5x})=x^2
The solution is x= 1/2 ,x=-3