What is the answer to solvefor a,f(a+2)=2^{(a+2)} ?

The answer to solvefor a,f(a+2)=2^{(a+2)} is a=-(\W(-(ln(2))/f)+2ln(2))/(ln(2))

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solvefor a,f(a+2)=2^{(a+2)}

solve for

a, f (a + 2) = 2^{(a + 2)}

a = - \frac{W ( - \frac{l n ( 2 )}{f} ) + 2 ln ( 2 )}{ln ( 2 )}

Solution steps

f (a + 2) = 2^{(a + 2)}

Prepare

f (a + 2) = 2^{(a + 2)}

for Lambert form:

f (a + 2) e^{l n (2) (- a - 2)} = 1

Rewrite the equation with

(- a - 2) ln (2) = u

and

a = - \frac{u + 2 ln ( 2 )}{ln ( 2 )}

f (- \frac{u + 2 ln ( 2 )}{ln ( 2 )} + 2) e^{u} = 1

Rewrite

f ((- \frac{u + 2 ln ( 2 )}{ln ( 2 )}) + 2) e^{u} = 1

in Lambert form:

e^{u} u = - \frac{ln ( 2 )}{f}

Solve

e^{u} u = - \frac{ln ( 2 )}{f} : u = W (- \frac{ln ( 2 )}{f})

u = W (- \frac{ln ( 2 )}{f})

Substitute back

u = (- a - 2) ln (2),

solve for

a

Solve

(- a - 2) ln (2) = W (- \frac{ln ( 2 )}{f}) : a = - \frac{W ( - \frac{l n ( 2 )}{f} ) + 2 ln ( 2 )}{ln ( 2 )}

a = - \frac{W ( - \frac{l n ( 2 )}{f} ) + 2 ln ( 2 )}{ln ( 2 )}

5^{x + 1} + 6 \cdot 5^{x} = 6

2^{2 x} = 31

1.0 6^{x} = 4.1

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

2^{2 x} = 11

What is the answer to solvefor a,f(a+2)=2^{(a+2)} ?
The answer to solvefor a,f(a+2)=2^{(a+2)} is a=-(\W(-(ln(2))/f)+2ln(2))/(ln(2))