What is the answer to (100^x-1)/(10^x+1)=9 ?

The answer to (100^x-1)/(10^x+1)=9 is x=1

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(100^x-1)/(10^x+1)=9

\frac{10 0 ^{x} - 1}{1 0 ^{x} + 1} = 9

x = 1

Solution steps

\frac{10 0 ^{x} - 1}{1 0 ^{x} + 1} = 9

Multiply both sides by

1 0^{x} + 1

\frac{10 0 ^{x} - 1}{1 0 ^{x} + 1} (1 0^{x} + 1) = 9 (1 0^{x} + 1)

Simplify

10 0^{x} - 1 = 9 (1 0^{x} + 1)

Apply exponent rules

(1 0^{x})^{2} - 1 = 9 (1 0^{x} + 1)

Rewrite the equation with

1 0^{x} = u

(u)^{2} - 1 = 9 (u + 1)

Solve

u^{2} - 1 = 9 (u + 1) : u = 10, u = - 1

u = 10, u = - 1

Substitute back

u = 1 0^{x},

solve for

x

Solve

1 0^{x} = 10 : x = 1

Solve

1 0^{x} = - 1 :

No Solution for

x \in R

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

\frac{3 ^{27}}{2 7 ^{3}} = 3^{k}

x, (\frac{1}{4})^{x} = 4

8 (4^{x}) - 9 (2^{x}) + 1 = 0

4^{(x)} - 12 \cdot 2^{(x)} + 35 = 0

x 143 = 12 e^{1.4 x + 1.3}

What is the answer to (100^x-1)/(10^x+1)=9 ?
The answer to (100^x-1)/(10^x+1)=9 is x=1
Solve for x: (100^x-1)/(10^x+1)=9
The solution is x=1