What is log_{sqrt(7)}(343x) ?

The solution to log_{sqrt(7)}(343x) is 6+2log_{7}(x)

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simplify log_{sqrt(7)}(343x)

simplify

lo g_{7} (343 x)

6 + 2 lo g_{7} (x)

Solution steps

lo g_{7} (343 x)

Apply radical rule:

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

7 = 7^{\frac{1}{2}}

= lo g_{7^{\frac{1}{2}}} (343 x)

Apply log rule:

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

lo g_{7^{\frac{1}{2}}} (343 x) = \frac{1}{\frac{1}{2}} lo g_{7} (343 x)

= \frac{1}{\frac{1}{2}} lo g_{7} (343 x)

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

= 2 lo g_{7} (343 x)

Simplify

lo g_{7} (343 x) : 3 + lo g_{7} (x)

= 2 (3 + lo g_{7} (x))

Expand

2 (3 + lo g_{7} (x)) : 6 + 2 lo g_{7} (x)

= 6 + 2 lo g_{7} (x)

\frac{1}{2} (lo g_{6} (s) + lo g_{6} (t))

lo g_{2} (\frac{4 x + 1}{x})

lo g_{5} (\frac{3 x ^{2}}{y ^{3}})

ln (\frac{7}{3})

\frac{1}{2} (6 ln (x) - 7 ln (y))

What is log_{sqrt(7)}(343x) ?
The solution to log_{sqrt(7)}(343x) is 6+2log_{7}(x)