What is the answer to solvefor x,4e^{2x+3}=7e^{3x-2} ?

The answer to solvefor x,4e^{2x+3}=7e^{3x-2} is x=2ln(2)+5-ln(7)

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solvefor x,4e^{2x+3}=7e^{3x-2}

solve for

x, 4 e^{2 x + 3} = 7 e^{3 x - 2}

x = 2 ln (2) + 5 - ln (7)

Decimal Notation

x = 4.44038 \dots

Solution steps

4 e^{2 x + 3} = 7 e^{3 x - 2}

Apply exponent rules

ln (4) + 2 x + 3 = ln (7) + 3 x - 2

Solve

ln (4) + 2 x + 3 = ln (7) + 3 x - 2 : x = 2 ln (2) + 5 - ln (7)

x = 2 ln (2) + 5 - ln (7)

5^{x} = 87

4^{2 x} = 3 2^{\frac{1}{2}}

5^{2 x} - 5^{x} + 1 = 0

5^{x} = 60

What is the answer to solvefor x,4e^{2x+3}=7e^{3x-2} ?
The answer to solvefor x,4e^{2x+3}=7e^{3x-2} is x=2ln(2)+5-ln(7)