What is the answer to 5log_{x}(16)=10 ?

The answer to 5log_{x}(16)=10 is x=4

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5log_{x}(16)=10

5 lo g_{x} (16) = 10

x = 4

Solution steps

5 lo g_{x} (16) = 10

Divide both sides by

5

lo g_{x} (16) = 2

Apply log rules

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

Multiply both sides by

lo g_{16} (x)

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

Simplify

1 = 2 lo g_{16} (x)

Switch sides

2 lo g_{16} (x) = 1

Divide both sides by

2

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

Apply log rules

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

3 lo g_{8} (x) = 1

lo g_{10} (x) (\frac{1}{27}) = - 3

lo g_{10} (x) + lo g_{10} (20) = 3

\frac{1}{2} = lo g_{10} (x)

t, lo g_{a} (t^{3}) = x