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3 years ago

Demonstrate two different ways to solve the equation 5^(2x+1) = 25.

Mathematics

1 answer:

Tanzania [10]3 years ago

3 0

Answer:

Step-by-step explanation:

Method 1: Taking the log of both sides...

So take the log of both sides...

5^(2x + 1) = 25

log 5^(2x + 1) = log 25 <-- use property: log (a^x) = x log a...

(2x + 1)log 5 = log 25 <-- distribute log 5 inside the brackets...

(2x)log 5 + log 5 = log 25 <-- subtract log 5 both sides of the equation...

(2x)log 5 + log 5 - log 5 = log 25 - log 5

(2x)log 5 = log (25/5) <-- use property: log a - log b = log (a/b)

(2x)log 5 = log 5 <-- divide both sides by log 5

(2x)log 5 / log 5 = log 5 / log 5 <--- this equals 1..

2x = 1

x=1/2

Method 2

5^(2x+1)=5^2

2x+1=2

2x=1

x=1/2

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PLS HELP

Colt1911 [192]

Answer:

y = -4x-21

Step-by-step explanation:

Hi there!

We want to write an equation of the line that passes through (-4, -5) and is parallel to y=-4x-1.

Parallel lines have the same slopes. So let's find the slope of y=-4x-1.

The line is written in the form y=mx+b, where m is the slope and b is the y intercept.

As -4 is in the place of where m should be, -4 is the slope of y=-4x-1.

It's also the slope of the line parallel to that line.

Right now, what we know about the line parallel to y=-4x-1 is that the slope of it is 4 and it passes through the point (-4, -5).

We can substitute those values into the formula for point-slope form, which is $y-y_1=m(x-x_1)$ , where m is the slope and $(x_1, y_1)$ is a point.

We can label the values of everything to help us avoid confusion.

m=-4

$x_1=-4\\y_1=-5$

Now substitute those values into the formula. Note: the formula contains SUBTRACTION, and we have NEGATIVE numbers. Hence,

$y--5=-4(x--4)$

Now simplify.

$y+5=-4(x+4)$

On the right side, do the distributive property.

y+5=-4x-16

Subtract 5 from both sides.

Hope this helps!

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