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Solve for x algebraically in 7^(-x+2) = 0.005, rounding your answers to three signicant digits. A) 4.32 B) 4.72 C) 5.12 D) 5.52 E) 5.92

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take log to base 7 on both sides 2-x = log 0.005 to base 7
use the base change formula then
I don't know why you've posted 3 times this same equation

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Other answers:

2-x = [log0.005/log 7]
Particularly, since people were helping you in the previous two versions
to the base 10
x -> 4.7228
aama100: that's some impressive calculator work. If only your tutoring skills were that good people might actually learn something.
Thank you him1618, I understand what I was supposed to do now. Its easier for me to figure out math when I see the equation in front of me because I am a visual learner.
thanks polpak
You can just use the base 10 log and you end up with the same thing \[log(7^{x-2}) = log(5/1000)\] \[\implies (x-2)log(7) = log(5) - log(1000)\] \[\implies x-2 = \frac{log(5) - 3}{log(7)} \implies x = \frac{log(5) - 3}{log(7)} + 2\]

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