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

Question

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

anonymous · Answer

take log to base 7 on both sides
2-x = log 0.005 to base 7

anonymous · Answer

use the base change formula then

anonymous · Answer

I don't know why you've posted 3 times this same equation

anonymous · Answer

2-x = [log0.005/log 7]

anonymous · Answer

Particularly, since people were helping you in the previous two versions

anonymous · Answer

to the base 10

anonymous · Answer

x -> 4.7228

anonymous · Answer

aama100: that's some impressive calculator work. If only your tutoring skills were that good people might actually learn something.

anonymous · Answer

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.

anonymous · Answer

thanks polpak

anonymous · Answer

You can just use the base 10 log and you end up with the same thing

$$log(7^{x-2}) = log(5/1000)$$
$$\implies (x-2)log(7) = log(5) - log(1000)$$
$$\implies x-2 = \frac{log(5) - 3}{log(7)} \implies x = \frac{log(5) - 3}{log(7)} + 2$$