PLZ HELP: Explain how to solve 3x − 4 = 6 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Question

Alexis1415 · Answer

So is this one just about explaining it or are there choices?

NicktheBlade16 · Answer

wants you to explain it

Alexis1415 · Answer

So if it's explaining, then the answer would be... x = 5.631 because,

$$3^(x-4) = 6$$

Then, Make sure you log aka use the logarithm, base 3 of both sides.

$$3^(x − 4) = \log₃ 6$$ 
$$x − 4 = \log₃ 6$$

After that make sure you use the correct change of the base formula (sometimes you can switch it up and make a mistake by using the wrong number).

$$x − 4 = \log 6 / \log 3$$

And finally we must solve for x.

$$x - 4 = \log 6 / \log 3$$

Which gives us our answer: 5.631

I hope this helps!

Alexis1415 · Answer

(the parenthesis in the problem are supposed to be exponents but it corrected to normal formula)

NicktheBlade16 · Answer

Ok, i dont understand it but im sure you are correct

Alexis1415 · Answer

Basically the log parts are the inverse function to the exponents so like for example 1000=10 and the base is 10 of 1000 is 3 or like how i would write/type log10 (1000) = 3. does that make a bit more sense?

NicktheBlade16 · Answer

actually. yes it does. Thank you again. :)

Alexis1415 · Answer

@nicktheblade16 wrote:

actually. yes it does. Thank you again. :)

ofc