What is the answer to 2^x-3^x-3^x=0 ?

The answer to 2^x-3^x-3^x=0 is x=-665/389

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2^x-3^x-3^x=0

2^{x} - 3^{x} - 3^{x} = 0

x = - \frac{665}{389}

Decimal Notation

x = - 1.70951 \dots

Solution steps

2^{x} - 3^{x} - 3^{x} = 0

Apply exponent rules

2^{x} - (2^{x})^{1.58496 \dots} - (2^{x})^{1.58496 \dots} = 0

Rewrite the equation with

2^{x} = u

u - (u)^{1.58496 \dots} - (u)^{1.58496 \dots} = 0

Solve

u - u^{1.58496 \dots} - u^{1.58496 \dots} = 0 : u = 0, u = (\frac{1}{2})^{\frac{665}{389}}

u = 0, u = (\frac{1}{2})^{\frac{665}{389}}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 0 :

No Solution for

x \in R

Solve

2^{x} = (\frac{1}{2})^{\frac{665}{389}} : x = - \frac{665}{389}

x = - \frac{665}{389}

4 (10)^{x} = 20

2 e^{2 x + 7} - 15 = 0

e^{3 x} = 4

6^{x - 2} = 36

4^{3 x - 2} = 4^{x + 1}