What is the answer to log_{x}(49)=2 ?

The answer to log_{x}(49)=2 is x=7

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log_{x}(49)=2

lo g_{x} (49) = 2

x = 7

Solution steps

lo g_{x} (49) = 2

Apply log rules

\frac{1}{lo g _{49} ( x )} = 2

Multiply both sides by

lo g_{49} (x)

\frac{1}{lo g _{49} ( x )} lo g_{49} (x) = 2 lo g_{49} (x)

Simplify

1 = 2 lo g_{49} (x)

Switch sides

2 lo g_{49} (x) = 1

Divide both sides by

2

lo g_{49} (x) = \frac{1}{2}

Apply log rules

x = 7

Verify Solutions:

x = 7

True

The solution is

x = 7

lo g_{2} (x + 7) + lo g_{2} (x) = 3

lo g_{3} (x + 3) + lo g_{3} (x + 5) = 1

1 - ln (x) = 0

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

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