I have no idea what the answer to this problem is, I'm given choices but I'm still lost. Given: log sub a 2=.4, log sub a 3 =.5, log sub a 5=.8 what is log sub a .01?
a)0.7
b)-0.6
c)1.44
d)-2.4
Please Help!
loga 10 = loga2 +loga5 you are given both of those. Calculate it.
loga .01 = loga (10^-2 = -2 loga 10
So what is -2*loga 10 ?
To find the value of -2*log(sub a)10, we need to use the given information and apply the properties of logarithms.
From the information given, we know that:
log(sub a)2 = 0.4,
log(sub a)3 = 0.5, and
log(sub a)5 = 0.8.
Now let's find log(sub a)10:
log(sub a)10 = log(sub a)(2 * 5)
= log(sub a)2 + log(sub a)5
= 0.4 + 0.8
= 1.2.
So, log(sub a)10 = 1.2.
Now let's find -2*log(sub a)10:
-2*log(sub a)10 = -2 * 1.2 = -2.4.
Therefore, the answer to log(sub a)0.01 is option (d) -2.4.