SOLUTION: How would you solve; 7^(2x+1)=4^(x-2)

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Question 936334: How would you solve; 7^(2x+1)=4^(x-2)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
7%5E%282x%2B1%29=4%5E%28x-2%29 .....since 7%5E%282x%2B1%29=7%5E%282x%29%2A7 and 4%5E%28x-2%29=4%5Ex%2F4%5E2, we have

7%5E%282x%29%2A7=4%5Ex%2F4%5E2

7%5E%282x%29%2A7=4%5Ex%2F4%5E2

7%5E%282x%29%2F4%5Ex=1%2F%287%2A4%5E2%29 .........use a logarithm

log%28%287%5E%282x%29%2F4%5Ex%29%29=log%28%281%2F%287%2A4%5E2%29%29%29

log%28%287%5E%282x%29%29%29-log%28%284%5Ex%29%29=log%281%29-log%28%287%2A4%5E2%29%29

...log%28%281%29%29=0

x%282log%28%287%29%29-log%28%282%5E2%29%29%29=2log%28%282%5E2%29%29-log%28%287%29%29

x%282log%28%287%29%29-2log%28%282%29%29%29=4log%28%282%29%29-log%28%287%29%29

x=%284log%28%282%29%29-log%28%287%29%29%29%2F%282%28log%28%287%29%29-log%28%282%29%29%29%29