find the exact value of the log : log subscript 4 1/64 = x
thanks
2007-11-04 10:10:05 · 6 answers · asked by Boo Radley 4 in Science & Mathematics ➔ Mathematics
4^x = 1/64
4^-x = 64
-x = 3
x = -3
2007-11-04 10:14:21 · answer #1 · answered by Bryan C 2 · 1⤊ 0⤋
log[base 4](1/64) = x
First, convert this to exponential form. Remember that
log[base b](a) = c if and only if b^c = a.
4^x = 1/64
But 64 can be expressed as 4^3, so
4^x = 1/4^3
And one over any positive exponent can be changed to that exponent negated.
4^x = 4^(-3)
Same base; equate the exponents.
x = -3
2007-11-04 10:21:35 · answer #2 · answered by Puggy 7 · 0⤊ 0⤋
log subscript 4 (1/64)=x
log subscript 4 ( 4^-3) =x
-3*log subscript 4 (4) = x , log subscrpt 4 (4 ) =1
x= -3
2007-11-04 10:20:23 · answer #3 · answered by Freddie 2 · 0⤊ 0⤋
Let log be log to base 4 in the following:-
log [ 4^(- 3) ] = x
(-3) log 4 = x
(-3) (1) = x
x = - 3
2007-11-04 10:25:39 · answer #4 · answered by Como 7 · 0⤊ 1⤋
4^x = 1/64
64 = 4^3 therefore 1/64 is 1/4^3 or 4^-3
so
4^x = 4^-3
so x = -3
2007-11-04 10:14:25 · answer #5 · answered by kissbreezy 3 · 0⤊ 0⤋
An integer between -2 and -4.
Think it out.
2007-11-04 10:14:58 · answer #6 · answered by UnknownD 6 · 0⤊ 0⤋