What is 3log_{a}(m)+2log_{a}(j)-4log_{a}(r) ?

The solution to 3log_{a}(m)+2log_{a}(j)-4log_{a}(r) is log_{a}((m^3j^2)/(r^4))

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simplify 3log_{a}(m)+2log_{a}(j)-4log_{a}(r)

simplify

3 lo g_{a} (m) + 2 lo g_{a} (j) - 4 lo g_{a} (r)

lo g_{a} (\frac{m ^{3} j ^{2}}{r ^{4}})

Solution steps

3 lo g_{a} (m) + 2 lo g_{a} (j) - 4 lo g_{a} (r)

Apply log rule:

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

3 lo g_{a} (m) = lo g_{a} (m^{3})

= lo g_{a} (m^{3}) + 2 lo g_{a} (j) - 4 lo g_{a} (r)

Apply log rule:

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

2 lo g_{a} (j) = lo g_{a} (j^{2})

= lo g_{a} (m^{3}) + lo g_{a} (j^{2}) - 4 lo g_{a} (r)

Apply log rule:

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

lo g_{a} (m^{3}) + lo g_{a} (j^{2}) = lo g_{a} (j^{2} m^{3})

= lo g_{a} (m^{3} j^{2}) - 4 lo g_{a} (r)

Apply log rule:

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

4 lo g_{a} (r) = lo g_{a} (r^{4})

= lo g_{a} (j^{2} m^{3}) - lo g_{a} (r^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{a} (j^{2} m^{3}) - lo g_{a} (r^{4}) = lo g_{a} (\frac{j ^{2} m ^{3}}{r ^{4}})

= lo g_{a} (\frac{m ^{3} j ^{2}}{r ^{4}})

2 (lo g_{6} (x) + lo g_{6} (y^{2})) - lo g_{6} (x + 2)

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

lo g_{7} (6) - lo g_{7} (x)

ln (\frac{39}{52})

ln (\frac{( \frac{5.5}{12} )}{10})

What is 3log_{a}(m)+2log_{a}(j)-4log_{a}(r) ?
The solution to 3log_{a}(m)+2log_{a}(j)-4log_{a}(r) is log_{a}((m^3j^2)/(r^4))