What is log_{sqrt(6)}(216x) ?

The solution to log_{sqrt(6)}(216x) is 6+2log_{6}(x)

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simplify log_{sqrt(6)}(216x)

simplify

lo g_{6} (216 x)

6 + 2 lo g_{6} (x)

Solution steps

lo g_{6} (216 x)

Apply radical rule:

a = a^{\frac{1}{2}}

6 = 6^{\frac{1}{2}}

= lo g_{6^{\frac{1}{2}}} (216 x)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{6^{\frac{1}{2}}} (216 x) = \frac{1}{\frac{1}{2}} lo g_{6} (216 x)

= \frac{1}{\frac{1}{2}} lo g_{6} (216 x)

\frac{1}{\frac{1}{2}} = 2

= 2 lo g_{6} (216 x)

Simplify

lo g_{6} (216 x) : 3 + lo g_{6} (x)

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

Expand

2 (3 + lo g_{6} (x)) : 6 + 2 lo g_{6} (x)

= 6 + 2 lo g_{6} (x)

lo g_{10} (\frac{x}{100 y ^{3}})

lo g_{5} (19 y)

lo g_{10} (\frac{( 23 \times 0.15 ) ^{2}}{234}) - 2

lo g_{10} (5 z^{5})

ln (\frac{x ( x ^{3} - 4 ) ^{5}}{( 1 - 2 x ) ^{3}})

What is log_{sqrt(6)}(216x) ?
The solution to log_{sqrt(6)}(216x) is 6+2log_{6}(x)