What is the answer to 2=log_{b}(16) ?

The answer to 2=log_{b}(16) is b=4

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2=log_{b}(16)

2 = lo g_{b} (16)

b = 4

Solution steps

2 = lo g_{b} (16)

Apply log rules

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

Multiply both sides by

lo g_{16} (b)

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

Simplify

2 lo g_{16} (b) = 1

Divide both sides by

2

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

Apply log rules

b = 4

Verify Solutions:

b = 4

True

The solution is

b = 4

2 lo g_{10} (x - 1) = lo g_{10} (x + 1)

ln (x - 4) + ln (7) = ln (x) + 2 ln (3)

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

3.2 = - lo g_{10} (x)

lo g_{10} (x) = - 4.1