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The graph = of a logarithmic function is shown below_ Find the equation of the function if the base of the log is an integer. (16 points)

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Find the value of the base $b$ so that the graph of $f(x)=\log _{b} x$ contains the given point.$$\left(\frac{1}{16}, 2\right)$$

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Find the indicated value of the logarithmic functions.$$\log _{16}(16)$$

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Finding Logarithmic Functions Find the function of the form $y=\log _{a} x$ whose graph is given.

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Transcript

Hello students here in this question: according to graph, we see that the domain for function is minus 2 to infinity. Therefore, let required function that is b y is equals to a into log base b of x, plus 2 plus b. Now take it as equation 1. Now we see that graph passes 2 point minus 1 and 3 point. Therefore putting in a bepissequation will get 3 is equal to a into log base b. Minus 1 plus 2 plus 3 implies will get. The value of c is equal to 3, as log base of 1 is equal to 0, which implies first equation will become, as is equal to a into log base b of x, plus 2 plus 3 is take it as equation. 2 also graph passes through .0 comma 4. The 4 putting above will get 4, is equal to a into log of base b, 0 plus 2 plus 3, which implies we’ll get the value of a log b of 2 is equals to 1. Take it as equation 3 now graph passes through .2 comma 5. Therefore, from second equation will get is equal to a into log of of 2 plus 2 plus 3, which implies we’ll get a log base b of 2 is equal to 1, which is same as third equation. Now, as we have given base of log is an…