Determine the value of each logarithm
a) Log(4)256
b) Log(2) 1/64
Thank you!
(4^2)2 or 4^4=256
log4(256)=4
log2 (1/64)=log2(1/8)^2=2*(-3)=-6
To determine the value of each logarithm, we need to use the logarithmic properties and evaluate the expressions.
a) Log(4)256: In this expression, we are looking for the logarithm of 256 with base 4. To find the value, we need to determine what power we need to raise 4 to in order to get 256.
Since 4^4 = 256, we can write Log(4)256 as Log base 4 of 4^4. By using the logarithmic property that states Log(base a) a^x = x, we can simplify the expression as 4. Therefore, Log(4)256 equals 4.
b) Log(2)1/64: In this expression, we are looking for the logarithm of 1/64 with base 2. Again, we need to determine what power we need to raise 2 to in order to get 1/64.
Rewriting 1/64 as 2^(-6), we can express the expression as Log(base 2) 2^(-6). Using the logarithmic property mentioned earlier, we know that Log(base a) a^x = x. Therefore, Log(2) 2^(-6) equals -6.
So, the values of the logarithms are:
a) Log(4)256 = 4
b) Log(2)1/64 = -6.