What is the answer to log_{2}(a)+log_{a}(4)=3 ?

The answer to log_{2}(a)+log_{a}(4)=3 is a=4,a=2

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log_{2}(a)+log_{a}(4)=3

lo g_{2} (a) + lo g_{a} (4) = 3

a = 4, a = 2

Solution steps

lo g_{2} (a) + lo g_{a} (4) = 3

Apply log rules

lo g_{2} (a) + \frac{2}{lo g _{2} ( a )} = 3

Rewrite the equation with

lo g_{2} (a) = u

u + \frac{2}{u} = 3

Solve

u + \frac{2}{u} = 3 : u = 2, u = 1

u = 2, u = 1

Substitute back

u = lo g_{2} (a),

solve for

a

Solve

lo g_{2} (a) = 2 : a = 4

Solve

lo g_{2} (a) = 1 : a = 2

a = 4, a = 2

Verify Solutions:

a = 4

True

, a = 2

True

The solutions are

a = 4, a = 2

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

lo g_{2} (2 x) = lo g_{2} (5 x + 4) - 3

ln (x^{7}) - ln (x^{2}) = 5

lo g_{8} (x) = - 1

lo g_{8} (x) = - 3

What is the answer to log_{2}(a)+log_{a}(4)=3 ?
The answer to log_{2}(a)+log_{a}(4)=3 is a=4,a=2
Solve for a: log_{2}(a)+log_{a}(4)=3
The solution is a=4,a=2