SOLUTION: Solve this equation. Please be sure to use the Change of Base Formula. {{{5 - 3^x = -40}}}

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Question 1166818: Solve this equation. Please be sure to use the Change of Base Formula.
5+-+3%5Ex+=+-40
Found 2 solutions by ikleyn, 750033275:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Why did you stop your trials ?


Try again . . .


/\/\/\/\/\/\/\/ 

Start from 

    5+-+3%5Ex = -40


Move the term  3%5Ex  from the left side to the right side, changing its sign.

Move the term -40  from the right side to the left side, changing its sign.


You will get

     5 + 40 = 3%5Ex.


It is the same as

     3%5Ex = 45.


Take logarithm base 10 of both sides.  You will get

    x%2Alog%2810%2C%283%29%29 = log%2810%2C%2845%29%29.


It implies

    x = log%2810%2C%2845%29%29%2Flog%2810%2C%283%29%29 = use your calculator = 3.465.    ANSWER

Solved.


------------------

I have read your last post.

Let me tell it honestly:   I never saw so low level knowledge in Math.

And never even could suggest that so low level is possible.


Have a nice day  (!)



Answer by 750033275(2) About Me  (Show Source):
You can put this solution on YOUR website!
As I solved this one on my own first, I got a non-real answer of 3.2362+2.8596i. Then, I notated down: "(Unless otherwise sign change to «log (3, 35)» ➡ ≈ 3.2362 (but without the “imaginary” solution add-in))".


I am really having a very rough time trying to know what that means, but if only I could recall on an example problem in my notes, recording the exact same steps to solve the equation more properly...


As of according to my TI-84 Plus calculator, in "Real" Mode, negative logarithms are not possible as a solution, because they are not real numbers, which is probably the same thing as "√-x", which is undefined!


So, the issue here is that I have no idea what "trials" I was recently told about or why did I stop them... Perhaps, I don't think I get the whole point!...if that's what my recent tutor was trying to say.


Thus, I was rather going to put in "no solution" or "Error" as the answer as it follows: "ERR: Nonreal Answer". To be honest, I have no idea what this is all about here, trying to solve equations relative to logarithms. I'm sure I have what I needed, but it just...doesn't feel right to me!... I wonder why...


Man, Pearson-Prentice Hall has some weird references going on in their interactive worksheets, I'll tell you what... And I have never heard of what to do next in my life regarding this topic. If they were trying to pull a joke on me, I will SO not be laughing... 😠


Anyhow, I wish I could explain how to do this question more properly, but it seems to me like I haven't understood one bit of this equation, and what do I come in here for to actually deserve this kind of "undesired punishment?" ...Never mind, actually. This might be something I can't tell anyone...


So, what was I supposed to do? Trying to put in "-log (45)" as a replacement for "log (-45)"? I don't know what else to say, but this is probably not the correct answer! Face it, I'm running ALL OUT of ideas!!! 😓💭


Wait! I think I can do this... 😤 😮 😯


First, I subtract 5 from both sides of this equation, to get -40 - 5 = -45.
-3%5Ex+=+-45


Then, I should check to see if both sides are in the same integer—negative!
-%283%5Ex%29+=+-%2845%29


Next, I was going to use the Change of Base Formula, but I've got a better idea!...
I should now turn -3^x=-45 into its logarithmic form.
The negative sign should be on the outside of the expression.
-%28log+%283%2C+45%29%29


I should now have an approximate solution of -%283.465%29.


This is equivalent to -3.465, but without the parenthesizing.


Using my calculator, x will give me approximately -3.465 as my final answer.


For your information, just in case if I forgot the steps on another problem like this one, I may come back to this solution at any time, unless if my recent tutor will check if I am either right or wrong.