10.) a. 4^-3/2= 0.125
b. 7^3= 343
2006-12-03 05:34:44 · 4 answers · asked by Katy J 1 in Science & Mathematics ➔ Mathematics
a)
log 4 0.125 = -3/2
b)
log 7 343 = 3
2006-12-03 05:36:42 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋
logs are exponents. they answer the question, "what exponent do I raise the base to giving this number".
in b) you are asking to find the log, you ask what exponent do I raise 7 to giving 343? The answer is 3. so the log base 7 (343) = 3. the log is 3. the exponent is 3.
in a), the base is 4. what exponent do you raise 4 to giving 0.125?
2006-12-03 05:43:06 · answer #2 · answered by grand_nanny 5 · 0⤊ 0⤋
a.
4^-3/2 = 0.125
log(a. 4^-3/2) = log(0.125)
log(a)+log(4^-3/2) = log(1/8)
log(a) + (-3/2)*log(4) = log(2^-3)
log(a) - 3/2*log(2²) = -3*log(2)
log(a) - 3*log(2) = -3*log(2) ........ if in the 2 base...
log(a) = 0
a = 1
b)
7^3= 343
log(7³) = log(343)
3*log(7) = log(343)
₢
2006-12-03 05:49:53 · answer #3 · answered by Luiz S 7 · 0⤊ 0⤋
A. log4 (.125) = -3/2
B. log7 (343) = 3
the 4 and the 7 should be the logs bases, meaning you put them in subscript..
2006-12-03 05:41:40 · answer #4 · answered by Roxanne 3 · 0⤊ 0⤋