Exponential integrated question
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Harry_the_cat
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These are what I call "hidden" quadratics.
What you have given is an expression not an equation as there is no equal sign. So it can't be solved, but it can be factorised.
The 49 and the 7 are big hints in this sort of expression because \(\displaystyle 49=7^2\).
I'll start you off:
\(\displaystyle 49^x - 7^{x+1} +12\)
\(\displaystyle (7^2)^x - 7^x * 7^1 +12\)
\(\displaystyle (7^x)^2 - 7*7^x +12\)
Now let \(\displaystyle a=7^x\)
\(\displaystyle a^2 -7a +12\)
Now factorise using the cross method if you wish then replace \(\displaystyle a=7^x\)
What you have given is an expression not an equation as there is no equal sign. So it can't be solved, but it can be factorised.
The 49 and the 7 are big hints in this sort of expression because \(\displaystyle 49=7^2\).
I'll start you off:
\(\displaystyle 49^x - 7^{x+1} +12\)
\(\displaystyle (7^2)^x - 7^x * 7^1 +12\)
\(\displaystyle (7^x)^2 - 7*7^x +12\)
Now let \(\displaystyle a=7^x\)
\(\displaystyle a^2 -7a +12\)
Now factorise using the cross method if you wish then replace \(\displaystyle a=7^x\)
Steven G
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No! You did not solve it (if you did you would know what x equals!), you factored it.
Dr.Peterson
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Actually, it isn't wrong to speak of "solving" a problem in general.
In fact, I don't generally find dictionaries mentioning "equation" in their definitions (though I think they should do so as one case among others). Here is one that does specifically mention solving an equation - and it also lists solving a problem under "mathematics".
In fact, I don't generally find dictionaries mentioning "equation" in their definitions (though I think they should do so as one case among others). Here is one that does specifically mention solving an equation - and it also lists solving a problem under "mathematics".
Harry_the_cat
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Not sure if I agree Dr P.
If the question was written as:
"1. Solve \(\displaystyle 49^x-7^{x+1} +12\)",
then that doesn't make sense … what are you meant to do?
If the question was:
"Solve the following problems:
1. Factorise \(\displaystyle 49^x-7^{x+1} +12\)"
then I suppose that's ok.
.
If the question was written as:
"1. Solve \(\displaystyle 49^x-7^{x+1} +12\)",
then that doesn't make sense … what are you meant to do?
If the question was:
"Solve the following problems:
1. Factorise \(\displaystyle 49^x-7^{x+1} +12\)"
then I suppose that's ok.
.