equation:
2log(base 3)X^4.278=(log(base7)X)+2
solve for X....
yeah, its really fun
2007-05-13 16:34:02 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
log3(x^2*4.278) = log7(x) + log7(49)
log3(x^8.556) = log7(49x)
Converting to a common log
log10(x^8.556) / log10(3) = log10(49x) / log10(7)
[8.556*log(7)/log(3) ] * logx = log49 + logx
[8.556*log(7)/log(3) - 1]*logx = log49
logx = log49 / [8.556*log(7)/log(3) - 1]
= 0.1194
x = 1.3165
2007-05-13 17:24:43 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
2*log(base 3)x^4.278 = (log(base7)x) + 2
Divide by 2
log(base 3)x^4.278 = 0.5*(log(base7)x) + 1
Raise 3 to both sides of equation
3^[0.5*(log(base7)x) + 1] = x^4.278
Take log to base 7 of both sides
[0.5*(log(base7)x) + 1]*log(base 7)3 = 4.278*log(base 7)x
To simplify, let y = log(base 7)x, z = log(base 7)3
[0.5*y) + 1]*z = 4.278*y
Combine y terms
(0.5z - 4.278)y = -z
y = -z/(0.5z - 4.278)
z = log(base 7)3 = 0.5646
Substitute z
y = 0.1413
Since y = log(base 7)x
x = 7^0.1413 = 1.3165
2007-05-13 17:46:23 · answer #2 · answered by sweetwater 7 · 0⤊ 0⤋
2 log_3 (x^4.278) = log_7 x + 2
<=> log_3 (x^8.556) = log_7 (49x)
<=> log_3 (x^8.556) = log_3 (49x) / log_3 7
<=> log_3 (x^(8.556 (log_3 7))) = log_3 (49x)
<=> x^(8.556 log_3 7) = 49x
<=> x^((8.556 log 7 / log 3) - 1) = 49
<=> x = 49^(1 / ((8.556 log 7 / log 3) - 1))
= 1.31646 to 5 d.p.
Check: LHS of original equation comes to 2.14130, RHS comes to 2.14130.
2007-05-13 16:50:44 · answer #3 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
you call this: FUN,
hicks
2007-05-13 16:45:40 · answer #4 · answered by myllur 4 · 0⤊ 1⤋
y is it fun?
2007-05-13 16:42:39 · answer #5 · answered by major 2 · 0⤊ 1⤋