Please help solve this exponential equation
75(1/5)^x/5 = 3
x = 10
x = 2
x =
x = 11

Question

Please help solve this exponential equation
75(1/5)^x/5 = 3  	
x = 10
	x = 2
	x = 
	x = 11

shegotsitall · Answer

attachment

shegotsitall · Answer

I figured it out, its 10.
So heres how you solve:

shegotsitall · Answer

(in case someone else is confused)

shegotsitall · Answer

1) Divide each side by 75, leave 3/75 in fraction form

shegotsitall · Answer

2) (1/5)^(x/5) is the same as 5^(-x/5)

shegotsitall · Answer

3) Cancel with a log on each side:

tkhunny · Answer

"Cancel with a log" doesn't mean anything.

shegotsitall · Answer

log5 (5^(-x/5)) = log5 (3/75)

This cancels out the left side to just (-x/5)
and the right side can be simplified with a calculator.
**A log  can cancel out an argument that is identical to the base of the log

shegotsitall · Answer

Now we have (-x/5) = -2

shegotsitall · Answer

That was step four so now step 5:
5) Now all we do is multiply each side by five:
-x = -10
and now divide by negative -1 each side

shegotsitall · Answer

The final answer is x= 10 ^^

shegotsitall · Answer

I wish I could award myself a metal QQ

tkhunny · Answer

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Keep in mind that there may be other ways to proceed.