SOLUTION: Hi Sir/Ma'am, Please assist. I am helping my daughter who is in high school. I bought the algebrator program but it does not solve this equation: 6*6^3x=36*6^x The book

Algebra ->  Equations -> SOLUTION: Hi Sir/Ma'am, Please assist. I am helping my daughter who is in high school. I bought the algebrator program but it does not solve this equation: 6*6^3x=36*6^x The book      Log On


   

Question 155813: Hi Sir/Ma'am,
Please assist.
I am helping my daughter who is in high school. I bought the algebrator program but it does not solve this equation:
6*6^3x=36*6^x
The book has the answer as x = 1/2 but I cannot get it.
I get x=3. What I have done is 6*6^3x divided by 36*6X equals 0
I simplyfy it and get 1*3x divided by 6*x equals 0
then transpose the 1/6 to get 2x=6
then x = 3
I forced the answer but it made no sense.
The books name is MATHEMATICS A COMPLETE COURSE WITH C.X.C QUESTIONS VOLUME 2. It has no ISBN. The author is Raymond Toolsie B Sc , MACP Published by CARIBBEAN EDUCATIONAL PUBLISHERS LTD PAGE 701 QUESTION 13 B

Please help
Reuel
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6%2A6%5E%283x%29=36%2A6%5Ex Start with the given equation


6%5E1%2A6%5E%283x%29=36%2A6%5Ex Rewrite 6 as 6%5E1


6%5E1%2A6%5E%283x%29=6%5E2%2A6%5Ex Rewrite 36 as 6%5E2


6%5E%281%2B3x%29=6%5E%282%2Bx%29 Multiply the monomials by adding the exponents.


Since the bases are equal, this means that the exponents are equal. So this means that 1%2B3x=2%2Bx


1%2B3x=2%2Bx Set the exponents equal to one another


3x=2%2Bx-1 Subtract 1 from both sides.


3x-x=2-1 Subtract x from both sides.


2x=2-1 Combine like terms on the left side.


2x=1 Combine like terms on the right side.


x=%281%29%2F%282%29 Divide both sides by 2 to isolate x.


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Answer:

So the answer is x=1%2F2 which in decimal form is x=0.5.