What is the answer to (5^{2x}-1)/(5^x+1)=4 ?

The answer to (5^{2x}-1)/(5^x+1)=4 is x=1

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(5^{2x}-1)/(5^x+1)=4

\frac{5 ^{2 x} - 1}{5 ^{x} + 1} = 4

x = 1

Solution steps

\frac{5 ^{2 x} - 1}{5 ^{x} + 1} = 4

Multiply both sides by

5^{x} + 1

\frac{5 ^{2 x} - 1}{5 ^{x} + 1} (5^{x} + 1) = 4 (5^{x} + 1)

Simplify

5^{2 x} - 1 = 4 (5^{x} + 1)

Apply exponent rules

(5^{x})^{2} - 1 = 4 (5^{x} + 1)

Rewrite the equation with

5^{x} = u

(u)^{2} - 1 = 4 (u + 1)

Solve

u^{2} - 1 = 4 (u + 1) : u = 5, u = - 1

u = 5, u = - 1

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 5 : x = 1

Solve

5^{x} = - 1 :

No Solution for

x \in R

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

8^{1 - 2 x} = 16

ln (e^{2 x}) = 2 x

4 e^{3 x} - 7 = 1

(e^{4})^{3 x} = e^{4} e^{3 x}

e^{t} - e^{- t} = 2

What is the answer to (5^{2x}-1)/(5^x+1)=4 ?
The answer to (5^{2x}-1)/(5^x+1)=4 is x=1
Solve for x: (5^{2x}-1)/(5^x+1)=4
The solution is x=1