2006-12-16 11:31:25 · 7 answers · asked by hans d 1 in Science & Mathematics ➔ Mathematics
5^(2x-7)=1/125
5^(2x-7)=5^-3
2x-7=-3
2x=4
x=2
2006-12-16 13:41:34 · answer #1 · answered by yupchagee 7 · 15⤊ 0⤋
Well, in general to solve a question of this nature you want to set up your equation so that the base on each side is the same, so in this case you want to convert 1/125 into 5^something:
1/125=1/(5^3)=(1/5)^3=5^(-3) and from there:
5^(2x-7)=5^(-3). Now this equation is true only if the powers on each side are the same so:
2x-7=-3 => 2x=4 => x=2, and there's your answer
2006-12-16 19:38:58 · answer #2 · answered by Michael J 5 · 0⤊ 0⤋
RHS = 1/5^3 = 5^(-3)
so 2x - 7 = - 3
or 2x = 4
or x = 2
2006-12-16 19:33:56 · answer #3 · answered by Mein Hoon Na 7 · 1⤊ 0⤋
5^(2x-7)=1/125
5^(2x-7) = 5-³
Working the expoents:
2x - 7 = -3
2x = 7 -3
2x = 4
x = 4:2
x = 2
Answer: {x E R | x = 2}
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2006-12-16 20:17:41 · answer #4 · answered by aeiou 7 · 0⤊ 0⤋
find a commen base which is 5 so it would be
5^(2x-7)=5^-3
the 5 council out so then its
2x-7=-3
add 7 to both sides(couciling out the -7)
2x=4
divide by 2 and
x=2
2006-12-16 19:49:08 · answer #5 · answered by jane doe 2 · 0⤊ 0⤋
Ok, let' see...
take the log of the expression and you will get
(2x-7)*log(5) = log(1/125)
(2x-7) = log(1/125)/log(5)
2x = 7 + log(1/125)/log(5)
x = (7+log(1/125)/log(5))/2
You can take it from here!
2006-12-16 19:36:48 · answer #6 · answered by alrivera_1 4 · 0⤊ 1⤋
5^(2x-7)=5^(-3)
2x-7=-3
adding 7
2x=4
dividing by 2
x=2
2006-12-16 19:34:21 · answer #7 · answered by raj 7 · 0⤊ 1⤋