What is the answer to log_{4}(256)+log_{s}(16)=6 ?

The answer to log_{4}(256)+log_{s}(16)=6 is s=4

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log_{4}(256)+log_{s}(16)=6

lo g_{4} (256) + lo g_{s} (16) = 6

s = 4

Solution steps

lo g_{4} (256) + lo g_{s} (16) = 6

Move

lo g_{4} (256)

to the right side

lo g_{s} (16) = 6 - lo g_{4} (256)

Apply log rules

\frac{1}{lo g _{16} ( s )} = 2

Multiply both sides by

lo g_{16} (s)

\frac{1}{lo g _{16} ( s )} lo g_{16} (s) = 2 lo g_{16} (s)

Simplify

1 = 2 lo g_{16} (s)

Switch sides

2 lo g_{16} (s) = 1

Divide both sides by

2

lo g_{16} (s) = \frac{1}{2}

Apply log rules

s = 4

Verify Solutions:

s = 4

True

The solution is

s = 4

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

lo g_{120000} (x) = 160000

2 lo g_{3} (6) + lo g_{3} (y) = 4

ln (x + 1) - ln (3) = 3

lo g_{6} (- x^{2} + 12 x) = 2

What is the answer to log_{4}(256)+log_{s}(16)=6 ?
The answer to log_{4}(256)+log_{s}(16)=6 is s=4
Solve for s: log_{4}(256)+log_{s}(16)=6
The solution is s=4