What is join 18/5 log_{4/5}(2) ?

The solution to join 18/5 log_{4/5}(2) is log_{4/5}(8*2^{3/5})

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join 18/5 log_{4/5}(2)

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\frac{18}{5} lo g_{\frac{4}{5}} (2)

lo g_{\frac{4}{5}} (8 \cdot 2^{\frac{3}{5}})

Decimal Notation

- 11.18262 \dots

Solution steps

\frac{18}{5} lo g_{\frac{4}{5}} (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{18}{5} lo g_{\frac{4}{5}} (2) = lo g_{\frac{4}{5}} (2^{\frac{18}{5}})

= lo g_{\frac{4}{5}} (2^{\frac{18}{5}})

2^{\frac{18}{5}} = 2^{3} \cdot 2^{\frac{3}{5}}

= lo g_{\frac{4}{5}} (2^{3} \cdot 2^{\frac{3}{5}})

2^{3} = 8

= lo g_{\frac{4}{5}} (8 \cdot 2^{\frac{3}{5}})

ln (y - 2) + ln (y + 2)

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

ln (\frac{48}{5})

ln \frac{2 ^{\frac{3}{2}}}{( 2 + \frac{3}{2} ) ^{\frac{3}{4}}}

\frac{1}{9} lo g_{6} (3)

What is join 18/5 log_{4/5}(2) ?
The solution to join 18/5 log_{4/5}(2) is log_{4/5}(8*2^{3/5})