SOLUTION: This question was on a test my teacher recently gave me, and needless to say, I got it wrong. I got stuck about half way through it. Can you please help me? <br> The original pro

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: This question was on a test my teacher recently gave me, and needless to say, I got it wrong. I got stuck about half way through it. Can you please help me? <br> The original pro      Log On

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Question 132314: This question was on a test my teacher recently gave me, and needless to say, I got it wrong. I got stuck about half way through it. Can you please help me?


The original problem looked like this:
+5%5Ex=2%5E%28x-6%29+


I first converted it to log form: xlog5 = x-6log2
Then punched in log5 and log2 into my calculator: x(.69897) = x-6(.30102)
Next, I distributed the -6: .69897x = x-1.80617
...and I'm stuck! Help, please!

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
+5%5Ex=2%5E%28x-6%29+ Start with the given equation


+log%2810%2C%285%5Ex%29%29=log%2810%2C%282%5E%28x-6%29%29%29+ Take the log of both sides


+x%2Alog%2810%2C%285%29%29=%28x-6%29%2Alog%2810%2C%282%29%29+ Use the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29 to rewrite both sides


+x%2Alog%2810%2C%285%29%29=x%2Alog%2810%2C%282%29%29-6%2Alog%2810%2C%282%29%29+ Distribute log%2810%2C%282%29%29 (note: you distributed the terms incorrectly)


+x%2Alog%2810%2C%285%29%29-x%2Alog%2810%2C%282%29%29=-6%2Alog%2810%2C%282%29%29+ Subtract x%2Alog%2810%2C%282%29%29 from both sides


+x%28log%2810%2C%285%29%29-log%2810%2C%282%29%29%29=-6%2Alog%2810%2C%282%29%29+ Factor out the GCF x


+x%28log%2810%2C%285%2F2%29%29%29=-6%2Alog%2810%2C%282%29%29+ Combine the logs on the left side using the identity log%28b%2C%28A%29%29-log%28b%2C%28B%29%29=log%28b%2C%28A%2FB%29%29


+x=-6%2Alog%2810%2C%282%29%29%2Flog%2810%2C%285%2F2%29%29+ Divide both sides by log%2810%2C%285%2F2%29%29 to isolate x

Now if you want an approximate answer, then simply use your calculator to get



x=-4.53882



So our answer is approximately x=-4.53882