Hello, archistrategos214!

If you'rejuststarting, these areawfulproblems!

I assume you know the basic properties of logarithms.

We have: .ln(x + 4) - ln(x - 2) - 2·ln(x - 2) .= .ln(x + 4) - 3·ln(x-2)1) .ln[(x+4)/(x-2)] - 2·ln(x - 2)

. . = .ln(x + 4) - ln(x - 2)³ .= .ln[(x + 4)/(x - 2)³]

That "base 9" really messes up the problem!2) .1 + log312 - ½·log318 - log92

Assuming you don't know the Base-Change Formula yet,

. . I'll show you a primitive approach.

Let .log9(2) = p . . . Then: .9^p .= .2 . → . (3²)^p .= .2 . → . 3^{2p} .= .2

. . Hence: .2p .= .log3(2) . → . p .= .½·log3(2)

Therefore: .log9(2) .= .½·log3(2)

The problem becomes: .log3(3) + log3(12) - ½·log3(18) - ½·log3(2)

. . = .log3(3·12) - ½[log3(18) + log3(2)] .= .log3(36) - ½[log3(18·2)]

. . = .log3(36) - ½log3(36) .= .½·log3(36) .= .log3(36^½) .= .log3(6)