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2 QUICK QUESTIONS PLEASE HELP ME I NEED THEM FOR THE MORNING!

the ______________ (fill in blank)
of logarithms state that log (xy)= logx + logy

solve the equation 6^3x+1= 2^2x-3, Leave in extact form

THANKS

1 answer

You must mean

6^(3x+1) = 2^(2x-3)

take log of both sides , use the rules of logs ....

(3x+1)(log6) = (2x-3)(log2)
(3log6)x + log6 = (2log2)x - 3log2
x(3log6 - 2log2) = -3log2 - log6
x = (log6 + 3log2)/(2log2 - 3log6
= - .970473 or appr -.97
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