What is the answer to e^{(6x)}-5e^{(3x)}+4=0 ?

The answer to e^{(6x)}-5e^{(3x)}+4=0 is x= 2/3 ln(2),x=0

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e^{(6x)}-5e^{(3x)}+4=0

e^{(6 x)} - 5 e^{(3 x)} + 4 = 0

x = \frac{2}{3} ln (2), x = 0

Solution steps

e^{(6 x)} - 5 e^{(3 x)} + 4 = 0

Apply exponent rules

(e^{x})^{6} - 5 (e^{x})^{3} + 4 = 0

Rewrite the equation with

e^{x} = u

(u)^{6} - 5 (u)^{3} + 4 = 0

Solve

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 1 : x = 0

x = \frac{2}{3} ln (2), x = 0

3^{2 x - 2} + 3^{x + 1} = 12

2^{2 x - 1} - 5 \cdot 2^{x + 1} + 32 = 0

1^{x} = 0

1^{x} = 1

4^{z} = 8

What is the answer to e^{(6x)}-5e^{(3x)}+4=0 ?
The answer to e^{(6x)}-5e^{(3x)}+4=0 is x= 2/3 ln(2),x=0