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Popular >

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

Solution

e^{x} = 2 e^{\frac{x}{2}} + 15

Solution

x = 2 ln (5)

+1

Decimal Notation

x = 3.21887 \dots

Solution steps

e^{x} = 2 e^{\frac{x}{2}} + 15

Apply exponent rules

e^{x} = 2 (e^{x})^{0.5} + 15

Rewrite the equation with

e^{x} = u

u = 2 u^{0.5} + 15

Solve

u = 2 u^{0.5} + 15 : u = 25

u = 25

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 25 : x = 2 ln (5)

x = 2 ln (5)

Popular Examples

e^{-10}= 1/(e^x)

e^{- 10} = \frac{1}{e ^{x}}

3^{-4x+3}=sqrt(3)

3^{- 4 x + 3} = 3

(1/125)^{3x-2}=625

(\frac{1}{125})^{3 x - 2} = 625

e^{(ln(0.3))t}=0.6

e^{(l n (0.3)) t} = 0.6

2^{2x}-20(2^x)+64=0

2^{2 x} - 20 (2^{x}) + 64 = 0

Frequently Asked Questions (FAQ)

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