math
posted by james on .
Find the value of each of the following. Leave your answers as fractions where appropriate. Do not change bases.
a) log4 (1/8)
B)10^(10log3)<superscript in brackets
c.2log3<subscript.9
d.log3<subscript.3^2x

4 = 2^2, so 2 = 4^(1/2)
1/8 = 1/2^3 = 2^3 = (4^1/2)^3 = 4^(3/2)
so, log4(1/8) = 3/2
10^(10log3) = 10^(log 3^10) = 10^(log 3^(10)) = 3^(10)
log3(9) = 2
2log3(.9) = log3(.9^2) = log3(.81)
log3(.81) = log3(81)  log3(100) = 4log3(100)
recall that logb(b^x) = x
log3(3^2x) = 2x