SOLUTION: how can i find the value of y? 4^2y + 4^(2y-1) = 4

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Question 657944: how can i find the value of y?
4^2y + 4^(2y-1) = 4
Found 3 solutions by Alan3354, Edwin McCravy, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
how can i find the value of y?
4^2y + 4^(2y-1) = 4
-----------------------
4%5E%282y-1%29%2A%284+%2B+1%29+=+4
4%5E%282y-1%29+=+4%2F5
(2y-1)*log(4) = log(0.8)
2y-1 = log(0.8)/log(4)
y = (log(0.8)/log(4) + 1)/2

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%282y%29 ++4%5E%282y-1%29 = 4

We use the principle that A%5E%28B%2BC%29=A%5EB%2AA%5EC on the second term:

4%5E%282y%29 + +4%5E%282y%294%5E%28-1%29 = 4

We change the 4%5E%28-1%29 to 1%2F4

4%5E%282y%29 ++4%5E%282y%29%2Aexpr%281%2F4%29 = 4

Multiply through by 4 to remove the fraction:

4%2A%22%224%5E%282y%29 + 4%2A%22%22+4%5E%282y%29%2Aexpr%281%2F4%29 = 4%2A%22%224

4%2A%22%224%5E%282y%29 + cross%284%29%2A%22%22+4%5E%282y%29%2Aexpr%281%2Fcross%284%29%29 = 4%2A%22%224

4%2A%22%224%5E%282y%29 + +4%5E%282y%29 = 16

The two terms on the left are like terms and combine as

5%2A%22%224%5E%282y%29 = 16

Then we divide both sides by 5


4%5E%282y%29 = 16%2F5

Now we take logs of both sides

log%28%284%5E%282y%29%29%29 = log%28%2816%2F5%29%29

We use the principle log%28%28A%5EB%29%29+=+B%2Alog%28%28A%29%29

2y%2Alog%28%284%29%29 = log%28%2816%2F5%29%29

Divide both sides by 2%2Alog%28%284%29%29

y = log%28%2816%2F5%29%29%2F%282log%28%284%29%29%29 = 0.4195179763

Edwin

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%282y%29+%2B+4%5E%282y-1%29+=+4
since 4%5E%282y%29%2F4 we have
4%5E%282y%29+%2B+4%5E%282y%29%2F4+=+4+...both sides multiply by 4
4%2A4%5E%282y%29+%2B+4%2A4%5E%282y%29%2F4+=4%2A+4+
4%2A4%5E%282y%29+%2B+4%5E%282y%29+=+16+
4%5E%282y%29%284+%2B+1%29+=+16+
5%2A4%5E2y+=+16+
4%5E%282y%29+=+16%2F5+

y+=+%284%2Alog%282%29-log%285%29%29%2F4%2Alog%282%29+

y+=+%284%2A+0.30102999566-0.69897000434%29%2F4%2A0.30102999566%29+

y+=+%281.20411998264-0.69897000434%29%2F1.20411998264%29+

y+=+%280.5051499783%29%2F1.20411998264%29+

highlight%28y+=0.42%29
cartoon%28+%0D%0A++number_line%28+600%2C+-10%2C+10%2C++0%2C+0.42+%29+%29+%29