To solve this logarithmic equation, we can use the properties of logarithms to condense the equation.
First, we can rewrite the equation using the property log (a) - log(b) = log(a/b):
log4(x) - log16(x) = 1/log4(x/16) = 1/4
Now, we can rewrite log4 as log base 2 (since 4 = 2^2):
log base 2 (x/16) = 1/4
Next, we can rewrite the equation using the definition of logarithms:
2^(1/4) = x/16
Now, we can solve for x:
2^(1/4) = x/12^(1/4) = (2^4)/12^(1/4) = 2^1/4 = 3
Therefore, there is no solution to the equation log4(x) - log16(x) = 1/4.
To solve this logarithmic equation, we can use the properties of logarithms to condense the equation.
First, we can rewrite the equation using the property log (a) - log(b) = log(a/b):
log4(x) - log16(x) = 1/
log4(x/16) = 1/4
Now, we can rewrite log4 as log base 2 (since 4 = 2^2):
log base 2 (x/16) = 1/4
Next, we can rewrite the equation using the definition of logarithms:
2^(1/4) = x/16
Now, we can solve for x:
2^(1/4) = x/1
2^(1/4) = (2^4)/1
2^(1/4) = 2^
1/4 = 3
Therefore, there is no solution to the equation log4(x) - log16(x) = 1/4.