log(base 4) 128=x solve for x?

Question

i know the answer is 3.5 but i do not know how to "prove it" simply pluging in is not allowed for me.

Answer 1

Log(base 4) 128=x
128 = 4^x
2^7 = (2^2)^x
2^7 = 2^(2x)
7 = 2x
7/2 = x
3.5 = x

Answer 2

so basically u are trying to find what power of 4 is 128.
you can use the change the bases thing, which gives us
log 128/log 4.
that is the easy way of doing things.

The full working should be:
(when its in brackets its a power)

Log(base4)128 = x
4(x) =128
2(2x) = 128
2(2x) = 2(7)
Because the bases are the same 2x = 7
X = 7/2
= 3.5

Answer 3

Assume in answer that "log" means log base 4
log 128 = x
128 = 4^x
2^7 = (2²)^(x)
2^7 = 2^(2x)
x = 3.5

Answer 4

128 = 2^7 = (2^2)^(7/2) = 4^3.5

so log(base 4) 128 = 3.5 as per definition of log

Answer 5

log(base 4) 128 = log(base 2^2) 2^7
simply if log(base a) a = 1 so same as
( 7/2 ) [log(base 2) 2] = 7 / 2 = 3.5

footnotes:
log(base a) a^n = n [log(base a) a] = n
log(base a^n) a = ( 1 / n ) [log(base a) a] = 1 / n

Answer 6

log(base 4) 128=x
128= 4 ^3.5

we know that log(base a) a=1

therefore,
log(base 4) 128 = 3.5 =x

x= 3.5

Answer 7

hey here is the solution.
log(base 4)128=log(base 2^2)2^7
= (7/2)log(base 2)2
= 3.5.
formulas used
log(base x^y)m= (1/y)log(base x)m;
log(base x)m^t= t log(base x)m;
also '^' means raised to the power of.

Answer 8

log(base 4) 128=x
which means...
4^x=128
so....
ln(4^x)=ln(128)
x ln(4) = ln(128)
x = ln(128)/ln(4)
x = 3.5