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

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) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Combine the logarithms using the identity

Multiply

Rewrite the logarithm in exponent form. In other words, use: ===>

Now take the square root of both sides

So our answer is

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

Using that, we can say:

But we also know that is equivalent to saying:

So, taking the square root of both sides, .

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

Hope this helps.
John
RELATED QUESTIONS
HELP =) ! resolving the Question 2570 (p200 - 250) : log of 9 to the base square root... (answered by rapaljer,venugopalramana)
In the equation logx 3+logx 5=4 what is the value of x, to the nearest... (answered by robertb)
Find the sum of the ap: logx(27/8), + logx(9/4), + logx(3/2)...(10 terms) Answer... (answered by math_tutor2020)
Express logx 4/9 in terms of logx... (answered by Tatiana_Stebko)
solve the equation:... (answered by Fombitz,Alan3354)
what is the answer to logx + log (x+15) =... (answered by user_dude2008)
what is the answer to log (x+2) - logx =... (answered by user_dude2008)
when logx=2logA-(1/2)logB, x is equal... (answered by nerdybill)
Solve the equation. log(x^4)=(logx)^2... (answered by lwsshak3)