SOLUTION: 1. Use the logarithm properties to present the expression log(x + 10) - log x as the logarithm of a single quantity. 2.Fill in the blank to make a true statement. To solve 3 x =

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1. Use the logarithm properties to present the expression log(x + 10) - log x as the logarithm of a single quantity. 2.Fill in the blank to make a true statement. To solve 3 x =      Log On

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Question 126801: 1. Use the logarithm properties to present the expression log(x + 10) - log x as the logarithm of a single quantity.
2.Fill in the blank to make a true statement. To solve 3 x = 26, we can take the logarithm of each side of the equation to get log (3 x ) = log (26). The power rule for logarithms would then provide a way of moving the variable x from its position as an __________ to the position of a coefficient.
3.Write the equation in logarithmic form (1/5)^-7=78125
4.Find the value of x: log3 9 = x

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
1. The log rule you need to apply is log%28b%2Ca%29-log%28b%2Cc%29=log%28b%2Ca%2Fc%29. So,
log%28x%2B10%29-log%28x%29=log%28%28x%2B10%29%2Fx%29

2. I'm presuming you meant to say 3%5Ex=26. The missing word is then 'exponent'

3. %281%2F5%29%5E-7=78125
This can be re-written as 5%5E7=78125. We know that if log%28b%2Cx%29=y then b%5Ey=x, so 5%5E7=78125 implies log%285%2C78125%29=7. Of course, you could also have left the equation in its original state and said log%28%281%2F5%29%2C78125%29=-7, but that is very messy. Monk wouldn't approve.

4. log%283%2C9%29=x => 3%5Ex=9. But we know that 9=3%5E2 so we can write 3%5Ex=3%5E2. Since we also know that b%5Em=b%5En if and only if m=n, x=2.