How can the indicated logarithm be found? Without a calculator❓

Mathematics

1 answer:

e-lub [12.9K]3 years ago

7 0

I guess you're supposed to write the expression on the right in terms of $A,B,C$ .

18. Notice that $729=9^3$ , so

$\log_8729=\log_89^3=3\log_89=3B$

20. Notice that $\dfrac{14}3=\dfrac{42}9=\dfrac{6\times7}9$ , so

$\log_8\dfrac{14}3=\log_8\dfrac{6\times7}9=\log_86+\log_87-\log_89=A+C-B$

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Write the equation of the line in fully simplified slope-intercept form.

Bad White [126]

Answer:

$y = -\frac{2}{5} x-6$

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula $m =\frac{y_2-y_1}{x_2-x_1}$ . Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):

$m = \frac{(-6)-(-4)}{(0)-(-5)} \\m = \frac{-6+4}{0+5} \\m = \frac{-2}{5} \\$

So, the slope of the line is $-\frac{2}{5}$ .

2) Next, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the $m$ , $x_1$ and $y_1$ into the formula.

Since $m$ represents the slope, substitute $-\frac{2}{5}$ in its place. Since $x_1$ and $y_1$ represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form:

$y-(-6) = -\frac{2}{5} (x-(0))\\y + 6 = -\frac{2}{5} x\\y = -\frac{2}{5} x-6$