What is the answer to 5*6^{-2x-1}-1=7 ?

The answer to 5*6^{-2x-1}-1=7 is x=-(ln(48/5))/(2ln(6))

Solve for x: 5*6^{-2x-1}-1=7

The solution is x=-(ln(48/5))/(2ln(6))

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5 \cdot 6^{- 2 x - 1} - 1 = 7

x = - \frac{ln ( \frac{48}{5} )}{2 ln ( 6 )}

Decimal Notation

x = - 0.63115 \dots

Solution steps

5 \cdot 6^{- 2 x - 1} - 1 = 7

Move

1

to the right side

5 \cdot 6^{- 2 x - 1} = 8

Divide both sides by

5

6^{- 2 x - 1} = \frac{8}{5}

Apply exponent rules

(- 2 x - 1) ln (6) = ln (\frac{8}{5})

Solve

(- 2 x - 1) ln (6) = ln (\frac{8}{5}) : x = - \frac{ln ( \frac{48}{5} )}{2 ln ( 6 )}

x = - \frac{ln ( \frac{48}{5} )}{2 ln ( 6 )}

2^{4 x} (3 2^{1 - x}) = 8^{x + 2}

5^{- x} = 25

2 7^{x - 1} = 9^{2 x}

5^{1 - 2 x} = 9

3^{x} = 500

What is the answer to 5*6^{-2x-1}-1=7 ?
The answer to 5*6^{-2x-1}-1=7 is x=-(ln(48/5))/(2ln(6))
Solve for x: 5*6^{-2x-1}-1=7
The solution is x=-(ln(48/5))/(2ln(6))