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Question 934781: Hello. I would like to know how to do this question and please if you could provided the work so I can see how to do these in the future. Thanks in advance for your help.
Solve for x. Describe the reason for each step you take.
27^(4x) = 9^(x + 1)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Your left and right members both are base-ten bases raised to variable powers. See how both bases are
3 raised to some integer powers.

%283%5E3%29%5E%284x%29=%283%5E2%29%5E%28x%2B1%29

3%5E%283%2A4x%29=3%5E%282%28x%2B1%29%29

That is simply both members being base of 3 raised to two different expressions of x.
The bases are equal and because the two members are stated equal, the powers are equal.

3%2A4x=2%28x%2B1%29

12x=2x%2B2
10x=2
highlight%28x=5%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Hello. I would like to know how to do this question and please if you could provided the work so I can see how to do these in the future. Thanks in advance for your help.
Solve for x. Describe the reason for each step you take.
27^(4x) = 9^(x + 1) 
27%5E%284x%29+=+9%5E%28x+%2B+1%29

%283%5E3%29%5E%284x%29+=+%283%5E2%29%5E%28x+%2B+1%29 ------- Changing 27 to 3%5E3, and 9 to 3%5E2

3%5E%283%284x%29%29+=+3%5E%282%28x+%2B+1%29%29 ------- Multiplying exponents since the bases are being raised from one power to another

3%5E%2812x%29+=+3%5E%282x+%2B+2%29 ------------ Completing multiplication of exponents

12x+=+2x+%2B+2 ------------------ Bases are equal, and so are their exponents

12x+-+2x+=+2

10x+=+2

x+=+2%2F10, or highlight_green%28x+=+1%2F5%29

You can do the check!! 

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