How to find the base variable of a power?

Asked Sep 21 '22 at 11:35

Active Sep 21 '22 at 11:35

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Hypothetically, if there was an equality

$(10)(1-x)^7 = 0$

How do I solve this for x? If I use log, I can see that $(1-x)$ becomes the base of the log and that just confuses me. If I set x = 1, then it seems to be solved. But it just seems like a very silly way of solving the question, because then it is true for all of these:

$(5)(1-x)^7 = 0$

$(10)(1-x)^6 = 0$

$(121230)(1-x)^9 = 0$

So I am taking a different example:

$(10)(1-x)^7 = 0.1$

where x = 1 is not the solution. How would I go about this? Can anyone please advise? Thank you.

asked Sep 21 '22 at 11:35

hridayns

1

Not logarithms, but another vertex of the triangle of power, namely $n$-th roots – Arthur Sep 21 '22 at 11:57
1

Hi @hridayns: Whatever be $a$ and $b$ you do have (when it makes sense) $$a(1-x)^7=b\Rightarrow 1-x=\sqrt[7]{\dfrac ba}$$ – Ataulfo Sep 21 '22 at 11:58
I think I understand. Thank you for "nth-roots" and the triangle of power, and also the notation. – hridayns Sep 21 '22 at 12:08

How to find the base variable of a power?

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