What is the answer to 1.5log_{x}(9)=3 ?

The answer to 1.5log_{x}(9)=3 is x=3

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1.5log_{x}(9)=3

1.5 lo g_{x} (9) = 3

x = 3

Solution steps

1.5 lo g_{x} (9) = 3

Divide both sides by

1.5

lo g_{x} (9) = 2

Apply log rules

\frac{1}{lo g _{9} ( x )} = 2

Multiply both sides by

lo g_{9} (x)

\frac{1}{lo g _{9} ( x )} lo g_{9} (x) = 2 lo g_{9} (x)

Simplify

1 = 2 lo g_{9} (x)

Switch sides

2 lo g_{9} (x) = 1

Divide both sides by

2

lo g_{9} (x) = \frac{1}{2}

Apply log rules

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

12.4 = - lo g_{10} (x)

lo g_{4} (2 x + 10) = 2

lo g_{4} (x + 4) = - 3

lo g_{2} (x - 3) = 6

lo g_{2} (x - 3) = 5