What is the answer to 6/(5^{-7x+2)}= 3/(3^{-12x+5)} ?

The answer to 6/(5^{-7x+2)}= 3/(3^{-12x+5)} is x=(ln(486)-2ln(5))/(12ln(3)-7ln(5))

Solve for x: 6/(5^{-7x+2)}= 3/(3^{-12x+5)}

The solution is x=(ln(486)-2ln(5))/(12ln(3)-7ln(5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{6}{5 ^{- 7 x + 2}} = \frac{3}{3 ^{- 12 x + 5}}

x = \frac{ln ( 486 ) - 2 ln ( 5 )}{12 ln ( 3 ) - 7 ln ( 5 )}

Decimal Notation

x = 1.54767 \dots

Solution steps

\frac{6}{5 ^{- 7 x + 2}} = \frac{3}{3 ^{- 12 x + 5}}

Apply exponent rules

ln (6) + (7 x - 2) ln (5) = (12 x - 4) ln (3)

Solve

ln (6) + (7 x - 2) ln (5) = (12 x - 4) ln (3) : x = \frac{ln ( 486 ) - 2 ln ( 5 )}{12 ln ( 3 ) - 7 ln ( 5 )}

x = \frac{ln ( 486 ) - 2 ln ( 5 )}{12 ln ( 3 ) - 7 ln ( 5 )}

Verify Solutions:

x = \frac{ln ( 486 ) - 2 ln ( 5 )}{12 ln ( 3 ) - 7 ln ( 5 )}

True

The solution is

x = \frac{ln ( 486 ) - 2 ln ( 5 )}{12 ln ( 3 ) - 7 ln ( 5 )}

e^{x + 7} = 5

10 0^{x + 5} = 1 0^{x^{2} - x + 12}

2 7^{2 x} = 3^{x - 7}

1600 = 1 0^{x}

4^{3 x} = 8^{x + 1}

What is the answer to 6/(5^{-7x+2)}= 3/(3^{-12x+5)} ?
The answer to 6/(5^{-7x+2)}= 3/(3^{-12x+5)} is x=(ln(486)-2ln(5))/(12ln(3)-7ln(5))
Solve for x: 6/(5^{-7x+2)}= 3/(3^{-12x+5)}
The solution is x=(ln(486)-2ln(5))/(12ln(3)-7ln(5))