What is the answer to 100^x+10^x=2 ?

The answer to 100^x+10^x=2 is x=0

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100^x+10^x=2

10 0^{x} + 1 0^{x} = 2

x = 0

Solution steps

10 0^{x} + 1 0^{x} = 2

Apply exponent rules

(1 0^{x})^{2} + 1 0^{x} = 2

Rewrite the equation with

1 0^{x} = u

(u)^{2} + u = 2

Solve

u^{2} + u = 2 : u = 1, u = - 2

u = 1, u = - 2

Substitute back

u = 1 0^{x},

solve for

x

Solve

1 0^{x} = 1 : x = 0

Solve

1 0^{x} = - 2 :

No Solution for

x \in R

x = 0

4^{n - 1} = 4096

4^{\frac{x}{6}} = 2

x, 2^{x} \cdot 2^{y} = 64

5 e^{x} = 30

2^{5 x - 3} = 6