Condense each expression to a single logarithm In z In x2

Condense each expression to a single logarithm. In z + In x/2 + ln y/2 5 ln x - 25 ln y Expand each logarithm. Log_5 (xy^6)^4 log_9 (x/y^5)^6 Evaluate each of the following. ln 3 - ln 1/2 -4e^2 e^x(e^-2)^-3x -3e^x e^3x e^-6x

Solution

7) lnz + (lnx)/2 +(lny)/2

= lnz + (1/2)lnx +(1/2)lny

=lnz + lnx^1/2 + lny^1/2

= ln(z *x^1/2*y^1/2)

8) 5lnx -25lny

= lnx^5 - lny^25

= ln(x^5)/y^25

9) log5[xy^6]^4

log5[x^4y^24]

log5[x^4] +log5[y^24]

=4log₅(x) + 24log₅(y)

10) log9(x/y^5)6

= log9(x^6y^30)

=log9(x^6) +log9(y^30)

= 6log9(x) + 30log9(y)