log (4rt. of 1000)
log (sqrt. 0.1) + 5 log (5rt.100)
2007-05-02 06:47:50 · 2 answers · asked by Lucky 3 in Science & Mathematics ➔ Mathematics
OK, since log a^b can be rewritten as a * log b, you can rewrite the first equation as:
log 4rt of 1000 = log 1000^1/4 = 1/4 log1000
since log1000 = 3 (10^3 = 1000), the answer is just 1/4 * 3 = 3/4.
For the second one, using the same principles,
log sqrt 0.1 + 5 log 5rt 100 = log 0.1^1/2 + 5 log 100^1/5 =
1/2 log 0.1 + log 100^(5*1/5) = 1/2 log 0.1 + log 100
= 1/2 * -1 + 2
= 2-1/2 = 3/2.
Better check my math but I'm pretty sure I did it right.
2007-05-02 07:02:45 · answer #1 · answered by Mark S, JPAA 7 · 0⤊ 0⤋
If the arguement (the stuff inside the () ) is of the form a^n, n being any number (including fractions), log a^n = n log a.
SOOOO.... log (1000)^1/4 = 1/4 log 1000 = 3/4
log(sqrt[0.1])+ 5 log (100)^1/5=
1/2 log 0.1 + 5(1/5) log 100 = -1/2 + 2 = 2 &1/2
2007-05-02 06:56:19 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋