answer and solution work log base 16 of 4?

log_16(4)
= log_(4^2)(4)
= [log_4(4)]/2
= 1/2

log_16 4
=log_16 sqrt(16)
=(1/2) x log_16 16
= 1/2

log base 16 4 = x
so 16^x=4
so x=1/2

Let x = log (base 16) 4
Then, 16^x = 4

16 raised to power .'what number' is 4?

since sqrt(16) =4 , 16^(1/2) = 4
square root and power 1/2 are the same.

x=1/2
log base 16 of 4 is 1/2

There are a few ways to do this.

Method 1: log_16 4 = ln4 / ln16 = ln4 / ln(4^2) = ln4 / 2ln4 = 1/2
Method 2: log_16 4 = log_16 16^(1/2) = (1/2) log_16 16 = (1/2)*1 = 1/2

Let log be log to base 16

x = log 4

16^x = 4

x = 1/2