If log(base8)3 = x and log(base4)7 = y, find an expression in terms of x and y for:
1) log(base2)21 and 2) log(base2)63
2007-12-01 11:28:42 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
answer is 1) 3x+2y and 2) 6x+2y
I would appreciate steps on how to get these answers.
2007-12-01 11:44:14 · update #1
thank you very much...you gave me the correct answer...merci
2007-12-01 11:56:23 · update #2
Remember the change of base rule for logs.
log[base a]x = log[base b]x / log[base b]a
___________
x = log[base 8]3 = log[base 2]3 / log[base 2]8
x = log[base 2]3 / 3
3x = log[base 2]3
y = log[base 4]7 = log[base 2]7 / log[base 2]4
y = log[base 2]7 / 2
2y = log[base 2]7
____________
1) log[base2]21 = log[base2](3*7)
= log[base2]3 + log[base2]7 = 3x + 2y
____________
2) log[base2]63 = log[base2](3²*7)
= log[base2]3² + log[base2]7
= 2*log[base2]3 + log[base2]7
= 2*(3x) + 2y = 6x + 2y
2007-12-01 11:49:50 · answer #1 · answered by Northstar 7 · 1⤊ 0⤋
log_2(21) = log_2(7x3)=log_2(7) + log_2(3)
= 1/2log_4(7) + 1/3log_8(3) = 1/2y + 1/3x
log_2(63) = log_2(7x9) = log_2(7) + log_2(9)
= 1/2y + 2/3x
2007-12-01 11:38:30 · answer #2 · answered by norman 7 · 0⤊ 1⤋