How do I solve this expression: log(base 4)256?

Answer 1

4^4=16*16=256 so the answer is just 4

Answer 2

A log is an exponent. Thus, your solution is the answer to the equation 4^x = 256. Since 4^4 = 256, your answer is 4.

Answer 3

log 256 base 4 = log 4^4 base 4(4*4*4*4 =256)

= 4log 4 base 4 (power rule says dat wen a power is dere u must
multiply it wid the log so take 4 to multiplied wid the log)
=4*1 ( log a to the base a =1 ie wen a no has the same no as the base it is equal to 1)
=4

or

log 256 to the base 4 = log 16^2 base 4
=2log 16 base 4
=2log 4^2 base 4
=2*2 log 4 base 4
=4*1
=4
hope u understood the nxt method also invovled the same type of steps

Answer 4

log (base4) 256
= log (base4) 4^4
= 4

'cause the base of the log and the base of the exponent "undo" each other due to the inverse property of logs and exponents with equal bases

Answer 5

log(base 4)256
= log(base 4) (4^4)
= 4 * [log(base 4) (4)] --- using log(base a)(b^c) = c*log(base a) (b)
= 4 * 1 --- using log(base a) (a) = 1
= 4

Answer 6

I know you this question has already been answered correclty. But another way of doing this is taking 256^1/4, and you can also get the answer that way.

Answer 7

first get the log and its sub by itself. to do that make the expression equal to a different number ( i beielve n or zero...can't remember)

then you just make the base the exponent and solve!

Answer 8

log (base b) a = ln(a) / ln(b)

So...
log (base 4) 256 = ln(256) / ln(4) = 4