How do find the x-intercept of #f(x)=2log4(x)#?

1 Answer
Ken C.
Sep 29, 2015

#(1/4, 0)#

Explanation:

The x-intercept occurs where the graph intercepts the x-axis - in other words, where #f(x) = 0#. So, all we have to do is set #f(x)# equal to #0# and solve for #x#. Let's do it:

#0 = 2log4x# (setting #f(x)# equal to 0)
#0 = log4x# (dividing by #2#)
#10^0 = 10^(log4x)# (10 to the power of both sides, to cancel out logarithm)
#1 = 4x# (simplifying; #10^0 = 1#, #10^(log4x) = 4x#)
#x = 1/4# (dividing by #4# to isolate #x#)

Thus, the x-intercept of #f(x) = 2log4x# occurs at the point #(1/4, 0)#.

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