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Use properties of logarithms to rewrite the expression

0 votes

 evaluate log_9 (x^2 -7x + 10) - log_9 (x^2 - 4) + log_9 (x + 2)=.

asked Dec 28, 2017 in PRE-ALGEBRA by anonymous
reshown Dec 28, 2017 by bradely

1 Answer

0 votes

log_9 (x^2 -7x + 10) - log_9 (x^2 - 4) + log_9 (x + 2)

                            =    log_9 (x^2 -5x - 2x + 10) - log_9 (x^2 - 2^2) + log_9 (x + 2)

                            =    log_9 [ x(x - 5) - 2(x - 5) ]  - log_9 [ (x + 2)(x - 2) ] + log_9 (x + 2)
                            =    log_9 [ (x - 5)(x - 2) ]  - log_9 [ (x + 2)(x - 2) ] + log_9 (x + 2)
                            =    log_9 { [(x - 5)(x - 2)] / [ (x + 2)(x - 2) ] } + log_9 (x + 2)
                            =    log_9 [(x - 5) / (x + 2)] + log_9 (x + 2)
                            =    log_9 { [(x - 5) / (x + 2)] (x + 2) }
                            =    log_9 (x - 5)
 
Hence
 
log_9 (x^2 -7x + 10) - log_9 (x^2 - 4) + log_9 (x + 2)   =   log_9 (x - 5)
answered Dec 28, 2017 by homeworkhelp Mentor

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