What is the answer to log_{x}(1000)= 3/2 ?

The answer to log_{x}(1000)= 3/2 is x=100

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log_{x}(1000)= 3/2

lo g_{x} (1000) = \frac{3}{2}

x = 100

Solution steps

lo g_{x} (1000) = \frac{3}{2}

Apply log rules

\frac{1}{lo g _{1000} ( x )} = \frac{3}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 2 = lo g_{1000} (x) \cdot 3

Simplify

2 = lo g_{1000} (x) \cdot 3

Switch sides

lo g_{1000} (x) \cdot 3 = 2

Divide both sides by

3

lo g_{1000} (x) = \frac{2}{3}

Apply log rules

x = 100

Verify Solutions:

x = 100

True

The solution is

x = 100

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

4 lo g_{10} (3 - 2 x) = - 1

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

x, lo g_{4} (x y) = - 2

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

What is the answer to log_{x}(1000)= 3/2 ?
The answer to log_{x}(1000)= 3/2 is x=100
Solve for x: log_{x}(1000)= 3/2
The solution is x=100