What is log_{(4pi(m^3))/3}(2m) ?

The solution to log_{(4pi(m^3))/3}(2m) is log_{(4pim^3)/3}(2)+log_{(4pim^3)/3}(m)

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simplify log_{(4pi(m^3))/3}(2m)

simplify

lo g_{\frac{4 π ( m ^{3} )}{3}} (2 m)

lo g_{\frac{4 π m ^{3}}{3}} (2) + lo g_{\frac{4 π m ^{3}}{3}} (m)

Solution steps

lo g_{\frac{4 π ( m ^{3} )}{3}} (2 m)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{\frac{4 π ( m ^{3} )}{3}} (2 m) = lo g_{\frac{4 π ( m ^{3} )}{3}} (2) + lo g_{\frac{4 π ( m ^{3} )}{3}} (m)

= lo g_{\frac{4 π ( m ^{3} )}{3}} (2) + lo g_{\frac{4 π ( m ^{3} )}{3}} (m)

Remove parentheses:

(a) = a

= lo g_{\frac{4 π m ^{3}}{3}} (2) + lo g_{\frac{4 π m ^{3}}{3}} (m)

ln (2 (ln (x) - 1))

20 lo g_{10} (\frac{0.05}{4 π \cdot 8 \cdot 1 0 ^{3}}) + 8 + 8

5 \cdot lo g_{10} (x) + 7 \cdot lo g_{10} (y)

3 ln (x) + \frac{1}{x} + ln (x + 1) + c

lo g_{10} (\frac{( 4 \cdot 1 0 ^{- 7} )}{( 1 0 ^{- 12} )})

What is log_{(4pi(m^3))/3}(2m) ?
The solution to log_{(4pi(m^3))/3}(2m) is log_{(4pim^3)/3}(2)+log_{(4pim^3)/3}(m)