Expand each logarithm. log₄5 x

Mathematics

1 answer:

Romashka [77]1 year ago

5 0

If the expression is log₄5 x,then the expansion of this will look like

(log 5+ log x)/log 4.

Given that the expression is log₄5 x.

We are required to find the expansion of the expression.

Base change theorem says that $log_{a}b$ = $log_{x}b/log_{x}a$ . We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₄5 x.

log₄5 x=(log 5+log x)/log 4

(We know that $log_{a}b$ = log b/ log a and log mn =log m +log n)

Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.

Learn more about base change theorem at brainly.com/question/14998693

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Find an equation for the perpendicular bisector of the line segment whose endpoints

TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

$\boxed{gradient = \frac{y1 -y 2}{x1 - x2} }$

Gradient of given line

$= \frac{1 - ( - 5)}{3 - ( - 9)}$

$= \frac{1 + 5}{3 + 9}$

$= \frac{6}{12}$

$= \frac{1}{2}$

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

$\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }$