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

The answer to log_{x}(3)=sqrt(3) is x=3^{1/(sqrt(3))}

Solve for x: log_{x}(3)=sqrt(3)

The solution is x=3^{1/(sqrt(3))}

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lo g_{x} (3) = 3

x = 3^{\frac{1}{3}}

Decimal

x = 1.88567 \dots

Solution steps

lo g_{x} (3) = 3

Apply log rules

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

Multiply both sides by

lo g_{3} (x)

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

Simplify

1 = 3 lo g_{3} (x)

Switch sides

3 lo g_{3} (x) = 1

Divide both sides by

3

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

Simplify

\frac{3}{3} : \frac{1}{3}

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

Apply log rules

x = 3^{\frac{1}{3}}

Verify Solutions:

x = 3^{\frac{1}{3}}

True

The solution is

x = 3^{\frac{1}{3}}

lo g_{\frac{1}{7}} (7 - x) = - 2

2 lo g_{7} (- 2 x) = 0

lo g_{10} (x - 15) - 2 = - lo g_{10} (x)

lo g_{10} (x) + lo g_{10} (x + 3) = 1

lo g_{0.25} (x) = \frac{5}{2}

What is the answer to log_{x}(3)=sqrt(3) ?
The answer to log_{x}(3)=sqrt(3) is x=3^{1/(sqrt(3))}
Solve for x: log_{x}(3)=sqrt(3)
The solution is x=3^{1/(sqrt(3))}