What is 2log_{a}(c)+3log_{a}(p)+1 ?

The solution to 2log_{a}(c)+3log_{a}(p)+1 is log_{a}(c^2p^3)+1

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simplify 2log_{a}(c)+3log_{a}(p)+1

simplify

2 lo g_{a} (c) + 3 lo g_{a} (p) + 1

lo g_{a} (c^{2} p^{3}) + 1

Solution steps

2 lo g_{a} (c) + 3 lo g_{a} (p) + 1

Apply log rule:

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

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

= lo g_{a} (c^{2}) + 3 lo g_{a} (p) + 1

Apply log rule:

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

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

= lo g_{a} (c^{2}) + lo g_{a} (p^{3}) + 1

Apply log rule:

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

lo g_{a} (c^{2}) + lo g_{a} (p^{3}) = lo g_{a} (c^{2} p^{3})

= lo g_{a} (c^{2} p^{3}) + 1

6 lo g_{2} (x - 5) - lo g_{2} (y) + lo g_{2} (x)

ln (6) - 2 + 2 ln (x)

ln (u) + ln (k)

\frac{1}{3} ln (2) + \frac{1}{3} ln (10)

\frac{ln ( 1.4 ) - 5 ln ( 1.05 )}{2 ln ( 1.05 )}

What is 2log_{a}(c)+3log_{a}(p)+1 ?
The solution to 2log_{a}(c)+3log_{a}(p)+1 is log_{a}(c^2p^3)+1