What is the answer to log_{X-1}(49)=2 ?

The answer to log_{X-1}(49)=2 is X=8

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log_{X-1}(49)=2

lo g_{X - 1} (49) = 2

X = 8

Solution steps

lo g_{X - 1} (49) = 2

Apply log rules

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

Multiply both sides by

lo g_{49} (X - 1)

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

Simplify

1 = 2 lo g_{49} (X - 1)

Switch sides

2 lo g_{49} (X - 1) = 1

Divide both sides by

2

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

Apply log rules

X - 1 = 7

Solve

X - 1 = 7 : X = 8

X = 8

Verify Solutions:

X = 8

True

The solution is

X = 8

ln (x) - ln (x + 1) = 4

4 = lo g_{10} (x)

lo g_{4} (2 x + 1) - lo g_{4} (x - 2) = 1

y, 3 ln (t) - ln (y) = 4

ln (12) - ln (x - 1) = ln (x - 2)