What is the answer to 3^x+3^{3x}=30 ?

The answer to 3^x+3^{3x}=30 is x=1

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3^x+3^{3x}=30

3^{x} + 3^{3 x} = 30

x = 1

Solution steps

3^{x} + 3^{3 x} = 30

Apply exponent rules

3^{x} + (3^{x})^{3} = 30

Rewrite the equation with

3^{x} = u

u + (u)^{3} = 30

Solve

u + u^{3} = 30 : u = 3

u = 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 3 : x = 1

x = 1

(23)^{x} = 1728

e^{4 x + 5} = 8

16 = 660 (0.5)^{\frac{x}{2}}

e^{3 x} = 100