SOLUTION: I have to solve 2log3x=4. (The 3 is subscript) I took the 2 from in front and used it as the power to 3. 3 squared is 9 and I don't understand how that equals 4.

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Question 1030138: I have to solve 2log3x=4. (The 3 is subscript)
I took the 2 from in front and used it as the power to 3. 3 squared is 9 and I don't understand how that equals 4.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is 2 * log3(x) = 4

this is equivalent to log3(x^2) = 4

this is true if and only if 3^4 = x^2

take the square root of both sides of this equation to get (3^4)^(1/2) = (x^2)^(1/2)

this becomes 3^2 = x

solve for x to get x = 9.

you can confirm that the solution is correct by replace x in the original equation and then evaluating that equation.

your original equation is 2 * log3(x) = 4

after you replace x with 9, this equation becomes 2 * log3(9) = 4

if you divide both sides of this equation by 2, you get log3(9) = 2

you can use the log base conversion formula to find log3(9).

log3(9) is equal to log10(9)/log10(3).

the log function of your calculator gives you log10.

the log base conversiion formula also gets you:

log3(9) = ln(9)/ln(3).

the ln function of your calculator gives you that.

in your calculator, do log(9)/log(3) and you will get 2.

in your calculator, do ln(9)/ln(3) and you will get 2.

here's some tutorials that may help you.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm

tutorials 42 through 48 deal with logarithmic equations and exponential equations which is what you are dealing with.

there's also lots of other good tutorials up there that may be helpful to you as well.

if you have any specific questions you still need to know about how to solve this problem, send me an email and i'll try to explain further.

the basic log formulas that you would be using on this problem are:

a * log(b) = log(b^a)

logb(a) = c if and only if b^c = a

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

I have to solve 2log3x=4. (The 3 is subscript)
I took the 2 from in front and used it as the power to 3. 3 squared is 9 and I don't understand how that equals 4.

------- Dividing both sides by 2 ------- Converting to EXPONENTIAL form As seen, 9 is correct
======== Checking ========
------ Substituting 9 for x 2 * 2 = 4 ------