What is the answer to 5^{x-1}=2+3/(5^{x-2)} ?

The answer to 5^{x-1}=2+3/(5^{x-2)} is x=2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5^{x-1}=2+3/(5^{x-2)}

5^{x - 1} = 2 + \frac{3}{5 ^{x - 2}}

x = 2

Solution steps

5^{x - 1} = 2 + \frac{3}{5 ^{x - 2}}

Apply exponent rules

5^{x} \cdot 5^{- 1} = 2 + 3 (5^{x})^{- 1} \cdot 5^{2}

Rewrite the equation with

5^{x} = u

u \cdot 5^{- 1} = 2 + 3 (u)^{- 1} \cdot 5^{2}

Solve

u \cdot 5^{- 1} = 2 + 3 u^{- 1} \cdot 5^{2} : u = 25, u = - 15

u = 25, u = - 15

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 25 : x = 2

Solve

5^{x} = - 15 :

No Solution for

x \in R

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

e^{3 x} - e^{2 (3 x)} = 0

1024 = 2^{x}

1 0^{x} = 100

y, x^{y} = 2

1 - 2 e^{x} = 0

What is the answer to 5^{x-1}=2+3/(5^{x-2)} ?
The answer to 5^{x-1}=2+3/(5^{x-2)} is x=2
Solve for x: 5^{x-1}=2+3/(5^{x-2)}
The solution is x=2