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

The answer to (10^x+1)/(1+10^{-x)}=100 is x=2

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(10^x+1)/(1+10^{-x)}=100

\frac{1 0 ^{x} + 1}{1 + 1 0 ^{- x}} = 100

x = 2

Solution steps

\frac{1 0 ^{x} + 1}{1 + 1 0 ^{- x}} = 100

Multiply both sides by

1 + 1 0^{- x}

\frac{1 0 ^{x} + 1}{1 + 1 0 ^{- x}} (1 + 1 0^{- x}) = 100 (1 + 1 0^{- x})

Simplify

1 0^{x} + 1 = 100 (1 + 1 0^{- x})

Apply exponent rules

1 0^{x} + 1 = 100 (1 + (1 0^{x})^{- 1})

Rewrite the equation with

1 0^{x} = u

u + 1 = 100 (1 + (u)^{- 1})

Solve

u + 1 = 100 (1 + u^{- 1}) : u = 100, u = - 1

u = 100, u = - 1

Substitute back

u = 1 0^{x},

solve for

x

Solve

1 0^{x} = 100 : x = 2

Solve

1 0^{x} = - 1 :

No Solution for

x \in R

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

2 e^{2 x} = 0

3^{2 x} = 3^{6}

4^{x} - 6 (2^{x}) = - 8

5^{2 x + 1} = \frac{1}{625}

(\frac{1}{9})^{x} = 27

What is the answer to (10^x+1)/(1+10^{-x)}=100 ?
The answer to (10^x+1)/(1+10^{-x)}=100 is x=2
Solve for x: (10^x+1)/(1+10^{-x)}=100
The solution is x=2