SOLUTION: Please help me solve this equation: 4^(x+1)-7=14

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Question 968341: Please help me solve this equation: 4^(x+1)-7=14
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4%5E%28x%2B1%29-7=14
4%5E%28x%2B1%29=14%2B7
4%5E%28x%2B1%29=21..........take log of both sides
log%284%5E%28x%2B1%29%29=log%2821%29
%28x%2B1%29log%284%29=log%283%2A7%29
x%2B1=%28log%283%29%2Blog%287%29%29%2Flog%284%29
x=%28log%283%29%2Blog%287%29%29%2Flog%282%5E2%29-1
x=%28log%283%29%2Blog%287%29%29%2F2log%282%29-1
x=%28log%283%29%2Blog%287%29%29%2F2log%282%29-1%2A2log%282%29%2F2log%282%29
x=%28log%283%29%2Blog%287%29-2log%282%29%29%2F2log%282%29...exact solution
x=%280.47712125472%2B+0.84509804-2%2A0.30102999566398%29%2F%282%2A0.30102999566398%29
x=%280.72015930339204%29%2F%280.60205999132796%29
x=1.1961587..............approximate solution






Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me solve this equation: 4^(x+1)-7=14
4%5E%28x+%2B+1%29+-+7+=+14

4%5E%28x+%2B+1%29+=+14+%2B+7

4%5E%28x+%2B+1%29+=+21 -------- Exponential form

log+%284%2C+21%29+=+x+%2B+1 ------ Logarithmic form

x+%2B+1+=+log%2821%29%2Flog%284%29 ------- Applying change of base

highlight_green%28x+=+log%2821%29%2Flog%284%29+-+1%29, or highlight_green%28x+=+1.196158711%29