SOLUTION: Express irrational solutions in exact form as a decimal rounded to three decimal places log2x+log6x=3 ((( log base 2 of x plus log base 6 of x=3)))

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Question 601555: Express irrational solutions in exact form as a decimal rounded to three decimal places
log2x+log6x=3 ((( log base 2 of x plus log base 6 of x=3)))
Answer by lwsshak3(11628) About Me  (Show Source):
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Express irrational solutions in exact form as a decimal rounded to three decimal places
log2x+log6x=3
convert to log base 2
log2(x)+log2(x)/log2(6)=3
log2(6)=log(6)/log(2)=2.585
log2(x)+log2(x)/2.585=3
LCD=2.585
2.585log2(x)+log2(x)=3*2.585≈7.755
place under single log
log2(x^2.585*x)=7.755
convert to exponential form
2^7.755=x^3.585
216.017=x^3.585
raise both side by 1/3.585 power
x=4.479