corresponding exponential & logarithmic functions quick check\nthe points (0,1), (1,14), and (2,196) all lie…

corresponding exponential & logarithmic functions quick check\nthe points (0,1), (1,14), and (2,196) all lie on the line of the exponential function ( f(x) = 14^x ). on which logarithmic function do the points (14,1) and (196,2) lie? (1 point)\n( circ g(x) = x^{14} )\n( circ g(x) = log_{14} x )\n( circ g(x) = log_{14x} )\n( circ g(x) = log x )

corresponding exponential & logarithmic functions quick check\nthe points (0,1), (1,14), and (2,196) all lie on the line of the exponential function ( f(x) = 14^x ). on which logarithmic function do the points (14,1) and (196,2) lie? (1 point)\n( circ g(x) = x^{14} )\n( circ g(x) = log_{14} x )\n( circ g(x) = log_{14x} )\n( circ g(x) = log x )

Answer

Explanation:

Step1: Recall inverse function property

The logarithmic function is the inverse of the exponential function $f(x)=14^x$. For an exponential function $f(x)=b^x$, its inverse logarithmic function is $g(x)=\log_b x$, which swaps the $x$ and $y$ coordinates of points on $f(x)$.

Step2: Verify with given points

For the point $(14,1)$: Substitute $x=14$ into $g(x)=\log_{14}x$, we get $\log_{14}14=1$, which matches. For the point $(196,2)$: Substitute $x=196$ into $g(x)=\log_{14}x$, we get $\log_{14}196=\log_{14}14^2=2$, which matches.

Answer:

$\boldsymbol{g(x) = \log_{14} x}$