What is the answer to ln(e^{2x}+3)=2x+ln(3) ?

The answer to ln(e^{2x}+3)=2x+ln(3) is x=(ln(3/2))/2

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ln(e^{2x}+3)=2x+ln(3)

ln (e^{2 x} + 3) = 2 x + ln (3)

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

Decimal Notation

x = 0.20273 \dots

Solution steps

ln (e^{2 x} + 3) = 2 x + ln (3)

f (x) = g (x),

then

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

e^{l n (e^{2 x} + 3)} = e^{2 x + l n (3)}

Simplify

e^{l n (e^{2 x} + 3)} : e^{2 x} + 3

Simplify

e^{2 x + l n (3)} : 3 e^{2 x}

e^{2 x} + 3 = 3 e^{2 x}

Solve

e^{2 x} + 3 = 3 e^{2 x} : x = \frac{ln ( \frac{3}{2} )}{2}

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

Verify Solutions:

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

True

The solution is

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

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

lo g_{a} (32) = - \frac{5}{2}

3.5 = - lo g_{10} (c)

N, x = lo g_{a} (N)

lo g_{3} (1 + lo g_{3} (2 x - 7)) = 1

What is the answer to ln(e^{2x}+3)=2x+ln(3) ?
The answer to ln(e^{2x}+3)=2x+ln(3) is x=(ln(3/2))/2