$b\in(0,\ 1)\ \cup\ (1,\ \infty)\\x > 0\\y\in\mathbb{R}\\--------------------------\\\\y=\log_bx\\\\For\ (1,\ 0)\to x=1,\ y=0.\ Substitute:\\\\\log_b1=0\to b^0=1\to b\in(0,\ 1)\ \cup\ (1,\ \infty)\\\\For\ (116,\ 2)\to x=116,\ y=2.\ Substitute:\\\\\log_b116=2\to b^2=116\to b=\sqrt{116}\\\to b=\sqrt{4\cdot29}\to b=\sqrt4\cdot\sqrt{29}\to b=2\sqrt{29}\\\\For\ (4,\ -1)\to x=4,\ y=-1.\ Substitute:\\\\\log_b4=-1\to b^{-1}=4\to b=\dfrac{1}{4}$

Different values of b.

<h3>Answer: There is no logarithmic function whose graph goes through given points.</h3><h3 />

Maybe the second point is $\left(\dfrac{1}{16},\ 2\right)$

Substitute:

$\log_b\dfrac{1}{16}=2\to b^2=\dfrac{1}{16}\to b=\sqrt{\dfrac{1}{16}}\to b=\dfrac{1}{4}$

<h3>Then we have the answer:</h3>

$\boxed{y=\log_{\frac{1}{4}}x}$

6 0

2 years ago

Solve for the indicated variable. <br><br> s = p + g/h for g.

Afina-wow [57]

Answer:

g = h(s-p)

Step-by-step explanation:

find the variable of interest — It is in the numerator of one of two terms on the right side of the equation
subtract every term on that side not containing the variable — subtract p to get s-p = g/h
multiply by the inverse of the coefficient of the variable of interest — the coefficient is 1/h, so we multiply by h to get ... h(s-p) = g
rearrange to the desired form. Here, it is probably OK to leave the parentheses and to simply put g on the left

g = h(s -p)

5 0

2 years ago

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