2006-10-02 19:10:12 · 14 answers · asked by jinx12 3 in Science & Mathematics ➔ Mathematics
2^x*5=10^x
2^x*5=(2*5)^x
(2^x)*5=(2^X)*(5^x)
5 = 5^x [cancelling 2^x from both sides as it can't be 0]
1 = 5^(x-1)
So (x - 1) = 0
or x = 1
2006-10-02 19:14:37 · answer #1 · answered by psbhowmick 6 · 3⤊ 0⤋
x=1
2006-10-03 06:43:50 · answer #2 · answered by Banglacat 2 · 0⤊ 0⤋
1 =x
2006-10-03 02:24:22 · answer #3 · answered by KYP 1 · 0⤊ 0⤋
The ans is 1.
I shall solve it
2^x*5 = 10^x
so 2^x * 5 = (2*5)^x = 2^x*5^x(as (a*b)^x = a^x * b^ x
devide both sided by 2^x we get 5 = 5^x
so x= 1
2006-10-03 02:19:32 · answer #4 · answered by Mein Hoon Na 7 · 1⤊ 0⤋
Wai spotted one answer, but here's a general solution method and also proves there is only one unique solution:
(2^x) *5=10^x
Noting that 10^x = (2*5)^x = (2^x) * (5^x) [from indices laws]
(2^x) *5= (2^x) * (5^x)
5 = 5^x
x=1
is the unique solution.
Alternatively you could also take logs to base 10: 2^x*5=10^x
=> x log 2 + log 5 = x log 10
log 5 = x (log 10 - log 2)
log 5 = x (log 5 + log 2 - log 2)
log 5 = x log 5
1 =x
2006-10-03 02:13:27 · answer #5 · answered by smci 7 · 1⤊ 0⤋
Take the natural log of both sides:
x*ln(2)+ln(5)=x*ln(10)
solve for x. Note that ln(10)-ln(2) is the same as ln(10/2) or ln(5).
2006-10-03 02:18:33 · answer #6 · answered by arbiter007 6 · 0⤊ 0⤋
2^x * 5 = 10^x
2^x * 5 = (2*5)^x
2^x * 5 = 2^x * 5^x
5 = 5^x
x=1
2006-10-03 02:16:37 · answer #7 · answered by Anonymous · 1⤊ 0⤋
Except the second answer, all answers up to here are true.
What is the answers of this equation?
2^X=X^2 ( X=2 & 4 But show the complet solution methode ).
2006-10-03 02:17:45 · answer #8 · answered by Anonymous · 0⤊ 0⤋
the girl is right it's 1 x=1
2006-10-03 02:22:48 · answer #9 · answered by need to know 1 · 0⤊ 0⤋
2^x*5=10^x
taking ln in both side
ln(5)+xln(2)=xln(10)
ln(5)=xln10-xln(2)
ln (5)=xln(10/2)
x=1
2006-10-03 05:34:41 · answer #10 · answered by Anonymous · 0⤊ 0⤋