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sergij07 [2.7K]
3 years ago
9

Use the definition of the logarithmic function to find x. log4 0.25=x x=?

Mathematics
1 answer:
GREYUIT [131]3 years ago
5 0
The answer is -1.

log_4(0.25)  =log_4( \frac{1}{4})= log_4(4^{-1} ) \\  \\ 
log(x^{a} ) = a*log(x) \\  \\ 
log_4(4^{-1} )= -1 *log_4(4) \\  \\ 
log_y(x) =  \frac{log(x)}{log(y)}  \\  \\ 
-1 *log_4(4) = -1* \frac{log(4)}{log(4)} = -1
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Which equation represents the line that is perpendicular to graph of 4x+3y=9 and passes through (-2,3)
goldfiish [28.3K]

4y = 3x + 18

Step-by-step explanation:

NOTE THAT A line that is perpendicular to another has a negative inverse of the slope of the other line. The products of their slopes, that is, is always -1

Therefore we can begin by finding the slope of this line defined by the function 4x+3y=9

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y = -4/3 x + 9/3

y = -4/3 x + 3

The slope of the  perpendicular line is, therefore;

¾  - this is the negative inverse of -4/3

Now that we know the slope, we need to find the y-intercept. This is where x = 0 and the line meets the y-axis;

i.e (0, y)

The other given point, where the line crosses  is (-2, 3). Remember that to get the gradient we use the formula;

Gradient = Δ y / Δ x

¾ = (3 – y) / (-2 – 0)

¾ = (3 –y) / -2  

¾ * -2 = 3 – y

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Remember the function of a straight line is given;

y = mx + c (m being slope and c being y-intercept)

y = 3/4 x + 9/2

4y = 3x + 18

Learn More:

brainly.com/question/2783474

brainly.com/question/14148974

#LearnWithBrainly

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