What is the answer to log_{4}(a)-5+6log_{a}(4)=0 ?

The answer to log_{4}(a)-5+6log_{a}(4)=0 is a=64,a=16

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log_{4}(a)-5+6log_{a}(4)=0

lo g_{4} (a) - 5 + 6 lo g_{a} (4) = 0

a = 64, a = 16

Solution steps

lo g_{4} (a) - 5 + 6 lo g_{a} (4) = 0

Apply log rules

lo g_{4} (a) - 5 + \frac{6}{lo g _{4} ( a )} = 0

Rewrite the equation with

lo g_{4} (a) = u

u - 5 + \frac{6}{u} = 0

Solve

u - 5 + \frac{6}{u} = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = lo g_{4} (a),

solve for

a

Solve

lo g_{4} (a) = 3 : a = 64

Solve

lo g_{4} (a) = 2 : a = 16

a = 64, a = 16

Verify Solutions:

a = 64

True

, a = 16

True

The solutions are

a = 64, a = 16

5 ln (x + 3) = 21

lo g_{10} (x - 5) = 1

lo g_{5} (x - 6) = 4

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

ln (- 1 + c) = ln (2)

What is the answer to log_{4}(a)-5+6log_{a}(4)=0 ?
The answer to log_{4}(a)-5+6log_{a}(4)=0 is a=64,a=16
Solve for a: log_{4}(a)-5+6log_{a}(4)=0
The solution is a=64,a=16