What is the answer to 27(3^{2x})+80(3^x)-3=0 ?

The answer to 27(3^{2x})+80(3^x)-3=0 is x=-3

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27(3^{2x})+80(3^x)-3=0

27 (3^{2 x}) + 80 (3^{x}) - 3 = 0

x = - 3

Solution steps

27 (3^{2 x}) + 80 (3^{x}) - 3 = 0

Apply exponent rules

27 (3^{x})^{2} + 80 \cdot 3^{x} - 3 = 0

Rewrite the equation with

3^{x} = u

27 (u)^{2} + 80 u - 3 = 0

Solve

27 u^{2} + 80 u - 3 = 0 : u = \frac{1}{27}, u = - 3

u = \frac{1}{27}, u = - 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = \frac{1}{27} : x = - 3

Solve

3^{x} = - 3 :

No Solution for

x \in R

x = - 3

x, e^{y - x^{2}} = 0

x, e^{y - x^{2}} = k

3^{x - 2} = 2^{x}

(\frac{1}{5})^{x} = 10

e^{x} = 24

What is the answer to 27(3^{2x})+80(3^x)-3=0 ?
The answer to 27(3^{2x})+80(3^x)-3=0 is x=-3
Solve for x: 27(3^{2x})+80(3^x)-3=0
The solution is x=-3