How do you solve log_9(-11x+2)=log_9(x^2+30)log9(−11x+2)=log9(x2+30)?

1 Answer
Jim G.
Mar 7, 2018

x=-4" or "x=-7x=−4 or x=−7

Explanation:

"using the "color(blue)"law of logarithms"using the law of logarithms

•color(white)(x)log_b x=log_b yrArrx=y∙xlogbx=logby⇒x=y

rArrx^2+30=-11x+2⇒x2+30=−11x+2

"express in "color(blue)"standard form"express in standard form

rArrx^2+11x+28=0larrcolor(blue)"in standard form"⇒x2+11x+28=0←in standard form

rArr(x+4)(x+7)=0⇒(x+4)(x+7)=0

x=4=0rArrx=-4x=4=0⇒x=−4

x+7=0rArrx=-7x+7=0⇒x=−7

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