Question

Simplify into one logarithm: 2logx+3logy

Answer 1

Express

2 log x + 3 log y

as one logarithm.

Apply the "log of.a power" rule for each term:

k log p = log(p^k) (p > 0)

then,

2 log x + 3 log y

= log(x^2) + log((y^3)

Now, use another log rule to bring those terms together:

"The sum of logarithms equals the logarithm of the product."

and you finally get

= log(x^2 * y^3) <----- there it is.

I hope this helps. =)