What is the answer to solvefor a,-4=2b+2log_{a}(2) ?

The answer to solvefor a,-4=2b+2log_{a}(2) is a=2^{-1/(b+2)}

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solvefor a,-4=2b+2log_{a}(2)

solve for

a, - 4 = 2 b + 2 lo g_{a} (2)

a = 2^{- \frac{1}{b + 2}}

Solution steps

- 4 = 2 b + 2 lo g_{a} (2)

Switch sides

2 b + 2 lo g_{a} (2) = - 4

Move

2 b

to the right side

2 lo g_{a} (2) = - 4 - 2 b

Divide both sides by

2

lo g_{a} (2) = - b - 2

Apply log rules

\frac{1}{lo g _{2} ( a )} = - b - 2

Multiply both sides by

lo g_{2} (a)

\frac{1}{lo g _{2} ( a )} lo g_{2} (a) = - b lo g_{2} (a) - 2 lo g_{2} (a)

Simplify

1 = - b lo g_{2} (a) - 2 lo g_{2} (a)

Switch sides

- b lo g_{2} (a) - 2 lo g_{2} (a) = 1

Factor

- b lo g_{2} (a) - 2 lo g_{2} (a) : - lo g_{2} (a) (b + 2)

- lo g_{2} (a) (b + 2) = 1

Divide both sides by

- (b + 2)

lo g_{2} (a) = - \frac{1}{b + 2}

Apply log rules

a = 2^{- \frac{1}{b + 2}}

Verify Solutions:

a = 2^{- \frac{1}{b + 2}}

True

The solution is

a = 2^{- \frac{1}{b + 2}}

lo g_{3} (x - 3) = 4

lo g_{a} (9) = (2)

lo g_{\frac{1}{2}} (x - 3) = - 3

2 ln (x) - 3 = 0

ln (x^{2}) - 1 = 0

What is the answer to solvefor a,-4=2b+2log_{a}(2) ?
The answer to solvefor a,-4=2b+2log_{a}(2) is a=2^{-1/(b+2)}