Asked by Anonymous
What is the exact value of x in the equation 3^(x+2)=5^(7x)?
Answers
Answered by
Steve
3^(x+2)=5^(7x)
(x+2) log3 = (7x) log5
xlog3 - 7x log5 = -log3
x(log3-7log5) = -log3
x = log3/(7log5-log3)
the log can be whatever base you like. Usually 10 or e
If you take logs base 3 or 5, then
x = 1/(7log<sub><sub>3</sub></sub>5 - 1)
or
x = log<sub><sub>5</sub></sub>3/(7-log<sub><sub>5</sub></sub>3)
(x+2) log3 = (7x) log5
xlog3 - 7x log5 = -log3
x(log3-7log5) = -log3
x = log3/(7log5-log3)
the log can be whatever base you like. Usually 10 or e
If you take logs base 3 or 5, then
x = 1/(7log<sub><sub>3</sub></sub>5 - 1)
or
x = log<sub><sub>5</sub></sub>3/(7-log<sub><sub>5</sub></sub>3)
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