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2 answers:
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Answer: 6x
Work Shown:
For each step, the logs are all base b. This is to save time and hassle of writing tricky notation of having to write the smaller subscript 'b' multiple times. The first rule to use is that log(x^y) = y*log(x) for any base of a logarithm. The second rule is that meaning that the log base of itself is 1
log(b^(6x)) = 6x*log(b) .... pull down exponent using the first rule above
log(b^(6x)) = 6x*1 .... use the second rule mentioned
log(b^(6x)) = 6x
Answer:
x=4
Step-by-step explanation:
<u>Step 1</u>:-
given the lengths of two sides of a right angle are represented by 2x and 3(x+1) and longest side is 17 units.
AB = 2x and BC = 3(x+1) and longest side AC= 17
by using Pythagoras theorem
<u>step 2:-</u>
The hypotenuse is longest side is AC = 17 units
(17)^2 = 4x^2 +9(X+1)^2
on simplification, we will use formula
289 = 4x^2 +9(x^2+2x+1)
finding factors 70 X 52 = 3640
Taking common , we get
13x(x-4)+70(x-4)=0
x-4=0 and 13x+70=0
x=4 and
x=4 and
we can not choose negative value so x value is 4
Final answer:- x = 4
<u>verification:-</u>
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289 = 4(4)^2+9(4+1)^2
289 = 64 +9(25)
289=289