What is the answer to 3^{x+5}=(3^{x+3}+8)/9 ?

The answer to 3^{x+5}=(3^{x+3}+8)/9 is x=-(ln(10))/(ln(3))-3

Solve for x: 3^{x+5}=(3^{x+3}+8)/9

The solution is x=-(ln(10))/(ln(3))-3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3^{x + 5} = \frac{3 ^{x + 3} + 8}{9}

x = - \frac{ln ( 10 )}{ln ( 3 )} - 3

Decimal Notation

x = - 5.09590 \dots

Solution steps

3^{x + 5} = \frac{3 ^{x + 3} + 8}{9}

Multiply both sides by

9

3^{x + 5} \cdot 9 = \frac{3 ^{x + 3} + 8}{9} \cdot 9

Simplify

3^{x + 5} \cdot 9 = 3^{x + 3} + 8

Subtract

3^{x + 3}

from both sides

3^{x + 5} \cdot 9 - 3^{x + 3} = 3^{x + 3} + 8 - 3^{x + 3}

Simplify

3^{x + 5} \cdot 9 - 3^{x + 3} = 8

Factor

3^{x + 5} \cdot 9 - 3^{x + 3} : 80 \cdot 3^{x + 3}

80 \cdot 3^{x + 3} = 8

Divide both sides by

80

3^{x + 3} = \frac{1}{10}

Apply exponent rules

(x + 3) ln (3) = ln (\frac{1}{10})

Solve

(x + 3) ln (3) = ln (\frac{1}{10}) : x = - \frac{ln ( 10 )}{ln ( 3 )} - 3

x = - \frac{ln ( 10 )}{ln ( 3 )} - 3

x, 8^{2 x} \cdot 3^{- \frac{1}{2}} \cdot y = 36

5^{x} + 36 x - 97 = 0

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

2^{3^{8^{x}}} = 512

6^{x} = 1

What is the answer to 3^{x+5}=(3^{x+3}+8)/9 ?
The answer to 3^{x+5}=(3^{x+3}+8)/9 is x=-(ln(10))/(ln(3))-3
Solve for x: 3^{x+5}=(3^{x+3}+8)/9
The solution is x=-(ln(10))/(ln(3))-3