Solve 6^x = 24

Question

Solve 6^x = 24

whpalmer4 · Answer

Do you know about logarithms?

anonymous · Answer

@calvinnguyen thank you so very much. :) 

@whpalmer4 I've just been stuck on exponential equations with unequal bases is all :) Thank you both! :)

anonymous · Answer

I've got one more for you guys if you are willing! :)

anonymous · Answer

Solve 5^(x + 5) = 9x

thomaster · Answer

@calvinnguyen 
The purpose of this site is not to solve people's problems. It's to explain how people can solve their problems. You're just giving the answer here and that's against the code of conduct.

whpalmer4 · Answer

Unless Calvin posted something and deleted it, I don't see how he's helped you here...what do you think the answer for the first problem is?  Looked like he posted 4 different values of $x$.

anonymous · Answer

The answer is x = 0.23 he helped me come to that conclusion and deleted it because he was giving me a direct answer.

whpalmer4 · Answer

No, $$6^{0.23} \ne 24$$

anonymous · Answer

what is your reasoning behind that statement @whpalmer4 ?

whpalmer4 · Answer

$$6^{0.23} \approx 6^{1/4}$$$$6^{1/4} = \sqrt{\sqrt{6}}$$

whpalmer4 · Answer

Look, if you raise a number to a power that is between 0 and 1, you get a smaller number!

anonymous · Answer

Ok! I'll take your word for it! Thank you!

whpalmer4 · Answer

$$6^0= 1$$$$6^1=6$$$$6^2=36$$Given those values, do you really think $$6^{0.23} = 24$$?!?

whpalmer4 · Answer

Raising a number to the $1/n$ power is the same as taking the $n$th root.  $$x^{1/2} = \sqrt{x}$$$$x^{1/3} = \sqrt[3]{x}$$$$x^{1/4} = \sqrt[4]{x}$$etc.

whpalmer4 · Answer

I would solve this problem using logarithms.

$$6^x = 24$$Take the log of both sides (any base, doesn't matter)
$$\log 6^x = \log 24$$$$x\log 6 = \log 24$$$$x = \frac{\log 24}{\log 6}$$
Punch that into your calculator and you'll get your answer.  Then do something important: verify your answer by plugging it into the original equation and see if it works!