HELP Condense the following into a single log or natural log

HELP

Condense the following into a single log or natural log: 3 log_7 x + 2 log_7 y - 4 log_7 z 2 ln (x^2 - 2) + 5 ln y

Solution

1) 3 log ₇ x + 2log ₇ y - 4 log ₇ z

applying property of log

log a+ log b = log (a*b)

log a -log b = log (a/b)

b log a = log a^b

= log ₇ x^3 *y^2 / z^4

2) 2 ln (x^2 -2 ) + 5 ln y

again using property of log

we get

ln {(x^2-2)^2 * y^5 }

3) 4 ln (x+1) + 2ln (x-1) - 3ln x

ln { (x+1)^4 * (x-1) ^2 } / x^3