How do you calculate log_2 512?

3 Answers
May 1, 2018

log_2(512)= 9

Explanation:

Notice that 512 is 2^9.
implies log_2(512) = log_2(2^9)
By the Power Rule, we may bring the 9 to the front of the log.
= 9log_2(2)

The logarithm of a to the base a is always 1. So log_2(2) = 1
=9

the value of log_(2)512=9

Explanation:

we need to calculate log_2(512)
512=2^9rArrlog_2(512)=log_2(2^9)
log_ab^n=nlog_ab rArrlog_(2)2^9=9log_(2)2
since log_(a)a=1rArrlog_(2)512=9

May 1, 2018

log_2 512 = 9" " because 2^9=512

Explanation:

Powers of numbers can be written in index form or log form.
They are interchangeable.

5^3 = 125 is index form: It states that 5xx5xx5 = 125

I think of log form as asking a question. In this case we could ask:

"Which power of 5 is equal to 125?"
or
"How can I make 5 into 125 using an index?"

log_5 125 =?

We find that log_5 125 = 3

Similarly:
log_3 81 =4" " because 3^4 =81
log_7 343 = 3" " because 7^3 =343

In this case we have:

log_2 512 = 9" " because 2^9=512

The powers of 2 are:

1, 2,4,8,16,32,64,128,256,512,1024

(From 2^0=1 up to 2^10 = 1024)

There is a real advantage in learning all the powers up to 1000, there are not that many and knowing them will make your work on logs and exponential equations SO much easier.