b Use the Laws of Logarithm to combine the expression 6 logs

b) Use the Laws of Logarithm to combine the expression: 6) logs( -1) log(-1) (ii) 4 log 1-1 log(r\' + 1) + 2 log(z-4)

Solution

i) log 5 ( x^2 -1 ) - log 5 ( x - 1)

lapplying law of logarithms

log a (m ) - log a ( n ) = log a ( m/n)

log 5 ( x^2 -1 ) - log 5 ( x - 1) = log 5 ( x^2 -1 ) / (x - 1)

log 5 ( x-1) ( x+1) / (x-1)

log ₅ ( x + 1 )

ii) 4 log x - 1/ 3 log ( x^2 +1 ) + 2 log ( x-1 )

4 log x = log x^4

1/3 log ( x^2 +1 ) = log (x^2 + 1)^1/3

2 log ( x- 1) = log (x-1)^2

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