SOLUTION: Solve and check: 2logm + 3logm=10

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Question 174941: Solve and check:
2logm + 3logm=10
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=log%2810%2C%28m%29%29 Note: if the base is not stated, the default base is 10


So we go from 2%2Alog%2810%2C%28m%29%29%2B3%2Alog%2810%2C%28m%29%29=10 to 2x%2B3x=10


2x%2B3x=10 Start with the given equation.


5x=10 Combine like terms on the left side.


x=%2810%29%2F%285%29 Divide both sides by 5 to isolate x.


x=2 Reduce.


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log%2810%2C%28m%29%29=2 Plug in x=log%2810%2C%28m%29%29


10%5E2=m Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


100=m Square 10 to get 100


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Answer:


So the solution is m=100