What is the answer to 2e^{2x}+15=13e^x ?

The answer to 2e^{2x}+15=13e^x is x=ln(5),x=ln(3/2)

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2e^{2x}+15=13e^x

2 e^{2 x} + 15 = 13 e^{x}

x = ln (5), x = ln (\frac{3}{2})

Decimal Notation

x = 1.60943 \dots, x = 0.40546 \dots

Solution steps

2 e^{2 x} + 15 = 13 e^{x}

Apply exponent rules

2 (e^{x})^{2} + 15 = 13 e^{x}

Rewrite the equation with

e^{x} = u

2 (u)^{2} + 15 = 13 u

Solve

2 u^{2} + 15 = 13 u : u = 5, u = \frac{3}{2}

u = 5, u = \frac{3}{2}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 5 : x = ln (5)

Solve

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

x = ln (5), x = ln (\frac{3}{2})

2^{2 x} = 500

x, 3^{4 x + 1} = 27

7^{- 2 x + 9} = 608

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

2^{x^{2} + x - 20} = 1

What is the answer to 2e^{2x}+15=13e^x ?
The answer to 2e^{2x}+15=13e^x is x=ln(5),x=ln(3/2)