In logarithmic form, (a) log base 4 of 16 equals 2, (b) log base 7 of 2401 equals 4, (c) log base 10 of 1000 equals 3, and (d) log base 10 of 0.0001 equals -4.
In each case, the given exponential equation can be converted into logarithmic form using the definition of logarithms. The logarithmic form for an equation of the form "a to the power of b equals c" is "log base a of c equals b."
(a) For 4 squared equals 16, we can express this in logarithmic form as "log base 4 of 16 equals 2." Therefore, C equals 16 and D equals 2.
(b) For 2401 equals 7 to the power of 4, the logarithmic form is "log base 7 of 2401 equals 4." Thus, E equals 2401 and F equals 4.
(c) The exponential equation 10 cubed equals 1000 can be written in logarithmic form as "log base 10 of 1000 equals 3." Consequently, G equals 1000 and H equals 3.
(d) The equation 0.0001 equals 10 to the power of -4 translates to "log base 10 of 0.0001 equals -4" in logarithmic form. Here, J equals 0.0001 and K equals -4.
The probable question may be:
Convert the exponential equations into logarithmic form:
(a) 4²= 16 is equivalent to log4 C= D.
C= ____ and D= ____
(b) 2401=7^4 is equivalent to log7 E = F.
E = _____ and F = ____
(c) 10³= 1000 is equivalent to log10 G = H.
G = ____ and H = _____
(d) 0.0001 = 10^-4 is equivalent to log10 J = K.
J = _____ and K = ____