What is the answer to log_{x}(4096)=6 ?

The answer to log_{x}(4096)=6 is x=4

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log_{x}(4096)=6

lo g_{x} (4096) = 6

x = 4

Solution steps

lo g_{x} (4096) = 6

Apply log rules

\frac{1}{lo g _{4096} ( x )} = 6

Multiply both sides by

lo g_{4096} (x)

\frac{1}{lo g _{4096} ( x )} lo g_{4096} (x) = 6 lo g_{4096} (x)

Simplify

1 = 6 lo g_{4096} (x)

Switch sides

6 lo g_{4096} (x) = 1

Divide both sides by

6

lo g_{4096} (x) = \frac{1}{6}

Apply log rules

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

- ln (- x) = 0

lo g_{2} (x) + 8 = 12

lo g_{a} (25) = 2

2 ln (x + 3) = ln (x + 1) + 3 ln (2)

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