What is the answer to log_{x}(243)= 5/6 ?

The answer to log_{x}(243)= 5/6 is x=729

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log_{x}(243)= 5/6

lo g_{x} (243) = \frac{5}{6}

x = 729

Solution steps

lo g_{x} (243) = \frac{5}{6}

Apply log rules

\frac{1}{lo g _{243} ( x )} = \frac{5}{6}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 6 = lo g_{243} (x) \cdot 5

Simplify

6 = lo g_{243} (x) \cdot 5

Switch sides

lo g_{243} (x) \cdot 5 = 6

Divide both sides by

5

lo g_{243} (x) = \frac{6}{5}

Apply log rules

x = 729

Verify Solutions:

x = 729

True

The solution is

x = 729

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

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

What is the answer to log_{x}(243)= 5/6 ?
The answer to log_{x}(243)= 5/6 is x=729
Solve for x: log_{x}(243)= 5/6
The solution is x=729