Solve log5(3/5) + 3log5(15/2)- log5(81/3)

Answer 1

First, simplify the expression using the properties of logarithms:

log5(3/5) + 3log5(15/2) - log5(81/3)

= log5(3) - log5(5) + 3(log5(15) - log5(2)) - log5(27)

= log5(3) - log5(5) + 3(log5(15) - log5(2)) - log5(3^3)

= log5(3) - log5(5) + 3(log5(15) - log5(2)) - log5(3 x 3 x 3)

= log5(3) - log5(5) + 3(log5(15) - log5(2)) - 3

Now, apply the logarithmic properties:

= log5(3) - log5(5) + log5((15)^3/(2^3)) - 3

= log5(3 x 15^3/2^3) - log5(5) - 3

= log5(3 x 3375/8) - log5(5) - 3

= log5(10125/8) - log5(5) - 3

= log5(1265) - log5(5) - 3

Since we cannot simplify the expression any further, this is the final solution.