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

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

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

The solution is x=(ln(7))/(ln(6))

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\frac{6 ^{x} - 7 ( 6 ^{- x} )}{2} = 3

x = \frac{ln ( 7 )}{ln ( 6 )}

Decimal Notation

x = 1.08603 \dots

Solution steps

\frac{6 ^{x} - 7 ( 6 ^{- x} )}{2} = 3

Multiply both sides by

2

\frac{6 ^{x} - 7 \cdot 6 ^{- x}}{2} \cdot 2 = 3 \cdot 2

Simplify

6^{x} - 7 \cdot 6^{- x} = 6

Apply exponent rules

6^{x} - 7 (6^{x})^{- 1} = 6

Rewrite the equation with

6^{x} = u

u - 7 (u)^{- 1} = 6

Solve

u - 7 u^{- 1} = 6 : u = 7, u = - 1

u = 7, u = - 1

Substitute back

u = 6^{x},

solve for

x

Solve

6^{x} = 7 : x = \frac{ln ( 7 )}{ln ( 6 )}

Solve

6^{x} = - 1 :

No Solution for

x \in R

x = \frac{ln ( 7 )}{ln ( 6 )}

5^{x} = 2 5^{10 x - 8}

2^{x^{2} + 7 x} = 8^{- 4}

x, 2 = e^{x y}

x, ln (e^{x} - 3) = 2

2^{x^{2} - 4 x - 12} = 8^{x + 2}

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