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

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

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

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

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

Decimal Notation

x = 3, x = - 0.5

Solution steps

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

f (x) = g (x),

then

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

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

Simplify

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

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

Solve

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

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

Verify Solutions:

x = 3

True

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

True

The solutions are

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

3 lo g_{5} (x^{2} + 9) - 6 = 0

lo g_{5} (8 - 7 x) = 3

lo g_{9} (x - 5) = 1 - lo g_{9} (x + 3)

ln (x^{\frac{1}{2}} - 4) = 3

4 ln (- 8 x - 2) - 9 = 8

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