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4 years ago

How do I solve ln(3x-5)=ln11+ln12

Mathematics

1 answer:

vladimir2022 [97]4 years ago

3 0

Answer:

$\large\boxed{x=\dfrac{137}{3}}$

Step-by-step explanation:

$\text{Use:}\\\\\ln a+\ln b=\ln(ab)\\\\\ln a=\ln b\Rightarrow a=b\\-------------\\Domain:\\\\3x-5>0\qquad\text{add 5 to both sides}\\\\3x>5\qquad\text{divide both sides by 3}\\\\x>\dfrac{5}{3}\\-----------------\\\\\ln(3x-5)=\n11+\ln12\\\\\ln(3x-5)=\ln(11\cdot12)\\\\\ln(3x-5)=132\iff3x-5=132\qquad\text{add 5 to both sides}\\\\3x=137\qquad\text{divide both sides by 3}\\\\x=\dfrac{137}{3}$

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4 years ago

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irina1246 [14]

Answer:

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3 years ago

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If x2 = 50, what is the value of x? (3 points)

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4 years ago

Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7, 2), and is parallel to the graph x + 3y = -5.

Elena-2011 [213]

Answer:

$B - A = -6$

Step-by-step explanation:

Given

Point: (-7,2)

x + 3y = -5

Required

Find B- - A in Ax + By = 3

To start with; we need to calculate the slope of x + 3y = -5

$x + 3y = -5$

Subtract x from both sides

$x - x + 3y = -5 - x$

$3y = -5 - x$

Divide both sides by 3

$\frac{3y}{3} = -\frac{5}{3} - \frac{x}{3}$

$y = -\frac{5}{3} - \frac{x}{3}$

The slope of the line is the coefficient of x

Slope = $- \frac{1}{3}$

The question says line Ax + By = 3 is parallel to line x + 3y = -5; This means that they have the same slope of $- \frac{1}{3}$

Having calculated the slope, next is to calculate the equation of the line using the following formula;

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$-\frac{1}{3} = \frac{y - 2}{x - -7}$

$-\frac{1}{3} = \frac{y - 2}{x +7}$

Cross Multiply

$-1(x+7) = 3(y-2)$

Open brackets

$-x - 7 = 3y - 6$

Add x to both sides

$x - x - 7 = 3y - 6 + x$

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Add 6 to both sides

$-7 + 6 = 3y -6 + 6 + x$

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Multipby both sides by -3

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$-9y - 3x = 3$

$-3x - 9y = 3$

Comparing the above to Ax + By = 3

$Ax = -3x\\A = -3$

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$B - A = -9 - (-3)$

$B - A = -9 + 3$

$B - A = -6$

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3 years ago