SOLUTION: In the equation logx 4 + logx 9 = 2, what is x equal to?

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Question 112835: In the equation logx 4 + logx 9 = 2, what is x equal to?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28x%2C+%284%29%29+%2B+log%28x%2C+%289%29%29++=+2 Start with the given equation


log%28x%2C+%284%2A9%29%29+=+2 Combine the logarithms using the identity log%28b%2C+%28x%29%29+%2B+log%28b%2C+%28y%29%29=log%28b%2C%28x%2Ay%29%29


log%28x%2C+%2836%29%29+=+2 Multiply


x%5E2=36 Rewrite the logarithm in exponent form. In other words, use: log%28b%2C%28x%29%29=y===> b%5Ey=x



sqrt%28x%5E2%29=sqrt%2836%29 Now take the square root of both sides


So our answer is

x=6

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
First let's start with the basic logarithmic identity:

log%28x%2Cab%29=log%28x%2Ca%29%2Blog%28x%2Cb%29

Using that, we can say:

log%28x%2C4%29%2Blog%28x%2C9%29=log%28x%2C4%2A9%29=log%28x%2C36%29=2

But we also know that log%28x%2C36%29=2 is equivalent to saying:

36=x%5E2

So, taking the square root of both sides, x=6.

Note that -6 which satisfies our equation 36=x%5E2, cannot be a solution because the definition of the logarithm function says that the base must be greater than zero.

Hope this helps.
John