Question

What is the solution(s) of the following logarithm?

Answer 1

\[2\log _{6}x = \log _{6}100\]

Answer 2

A. -10 only
B. 10 only
C. -10 and 10
D. no solution

Answer 3

Would I first use the power property to make the equation\[\log _{6}x ^{2} = \log _{6}100\]then use the property of equality to cancel out the "log6"s, making the equation\[x ^{2} = 100\]?

Answer 4

So would it be + or - 10? Yes?

Answer 5

Or would it be just 10? Or just -10?

Answer 6

Do you have graph calculation?

Answer 7

I don't believe so.

Answer 8

Aw ok. Ok. From your work, you got x = -10 and 10, right? Ok, Let make sure it is right by plug -10 and 10 into original equation: \(2\log_6 x = \log 100\)

Is \(2\log_6(-10)\) valid?

Answer 9

Well, that equals\[\log _{6}(-10)^{2}\]or\[\log _{6}100\]which equals about 2.57.. what makes it valid or invalid?

Answer 10

Well, you can also do \(\log_6100 = log_610^2 = 2log_610\)
Then divide both sides by 2 and you get \(\log_6 x = \log_6 10\).

Then use the property of equality to cancel out the logarithm, which making the equation \(\boxed{x=10}\)

Also, calculate \(2\log_6(-10)\). What does the calculator say?
Yes, it's undefined, so x \(\neq\) -10.

Is this clear?

Answer 11

Yes! Thank you very much!