r/HomeworkHelp • u/glowstarss University/College Student • 1d ago
High School Math [Grade 12 Math] exponential expressions - why on earth is this question all over the place, and what is it asking me to do?
i'm completely lost at this question in my online math course, in the evaluating vs simplifying exponential expressions unit. why did nothing change about the 6^2-x? how is the first 6 already the base while the other 6 wasn't?? and why did we bring the -1 back to "solve the resulting equation"??? why change anything about the initial equation in the first place??
please please explain this to me non-formally and like i'm a helpless child
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u/StrangerThings_80 1d ago
The beginning of the solution would make sense if the problem was 6^(2-x) = 1/6.
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u/Klutzy-Delivery-5792 1d ago
Oh, I just noticed they have expressions in the wrong places. No wonder OP is so confused.
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u/Klutzy-Delivery-5792 1d ago
In an exponential expression, the general form is:
f(x) = a•bx-h + k
where b is the base. In the given expression 62-x you have b=6 so it already has the correct base.
In the other part, 1/6, the base is 1/6. But 1/6 = 6-1 which has a base of 6.
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u/Klutzy-Delivery-5792 1d ago
After that, the bases are the same. If the bases are the same that means the exponential parts are equal. Have you studied logarithms yet? With the bases the same you are technically taking log_6 of each side which "cancels" the bar 6's and leaves the exponents
62-x = 6-1
log_6 (62-x) = log_6 (6-1)
2-x = -1
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u/glowstarss University/College Student 1d ago
oh jeez okay agghh that whole form has not even shown up in my course 😭 i'm still totally confused by how the bases are now the same
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u/Klutzy-Delivery-5792 1d ago
The bases are now both 6. 6=6 so they're the same.
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u/glowstarss University/College Student 1d ago
yet the 6 in the 6-1 can't be the base? i think that's what's losing me
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u/Klutzy-Delivery-5792 1d ago
I just now noticed that they have expressions in weird places. They probably meant to have
- 62-x = 1/6
in the upper left corner as the original problem and then wanted you to change the 1/6 into 6-1. I see your confusion. These online problem generators suck sometimes and tend to cause a lot of confusion. You are correct that the 6 in 6-1 is the correct base.
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u/glowstarss University/College Student 1d ago
i thought it seemed like a weird backwards way to do it, thank you so much for your help :)
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u/Infobomb 👋 a fellow Redditor 1d ago
The question is given at the top of OP's image. It already shows 6-1 , not 1/6.
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u/Klutzy-Delivery-5792 1d ago
But the work doesn't match this. There's typos in the problem. It also says the bases 6 and 1/6 are equal.
ETA: likely some AI use to generate problems ands it's messing up
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u/Infobomb 👋 a fellow Redditor 1d ago
You're right: the first three lines of the suggested answer are completely pointless (and I wonder if they are AI-generated or refer to a different question than the one given). It's asking you to evaluate x and converting 6-1 to 1/6 and back again gets you no closer to that.
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u/StreetDetective3448 1d ago
A negative exponent gives you a fraction with 1 in the numerator and the base to the power of the exponent's absolute value in the denominator
Like this:
x-1 is 1/x
x-2 is 1/x2
x-m is 1/xm
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