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3 years ago

Solve by using the given theorems of logarithms. log 5 + log 2 =

Mathematics

1 answer:

madam [21]3 years ago

5 0

Answer:

Step-by-step explanation:

Using the rule of logarithms

log x + log y ⇔ log(xy)

$log_{b}$ b = 1

Hence

log 5 + log 2 = log(5 × 2) = log 10 = 1

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Write the slope intercept for 2x - 5y = -5

xxMikexx [17]

Answer:

the slope is $\frac{2}{5}$ and the y-intercept is $1$

Step-by-step explanation:

if we can get it to $y=mx+b$ form, then it's easy since the slope is $m$ and the y-intercept is $b$

solve $2x-5y=-5$ for $y$

$2x-5y=-5$

minus 2x from both sides

$-5y=-2x-5$

divide by -5 both sides

$5y=\frac{2}{5}x+1$

match

$m=\frac{2}{5}$ and $b=1$

the slope is $\frac{2}{5}$ and the y-intercept is $1$

8 0

4 years ago

Read 2 more answers

Lamar is solving the equation x2−12x=−6 by completing the square. Which shows Lamar's next step and the solution to the equation

Lyrx [107]

x2 - 12x = -6

Your next step would be to add 36 to both sides.

x2 - 12x + 36 = 30

In completing the square, we divide the term before x by 2, and then square it and add it to both sides.

12 / 2 = 6

6^2 = 36

That would be the next step.

5 0

4 years ago

Olivia orders 24 cupcakes and a layer cake. The layer cake costs $16, and the total cost of the order is $52. What is the cost o

exis [7]

Answer:

The total cost was $52. Subtracting out the cost of the layer cake ($16) leaves us with $36 to pay for the 24 cupcakes. This means that each cupcake must have cost $1.50 ( = $36 / 24 cupcakes ).

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find an equation of a line with the x- and y-intercepts below. Use exact fractions when necessary.

tamaranim1 [39]

Answer:

$y=\frac{5}{7}x-5$

Step-by-step explanation:

All lines in the plane are of the form

y = mx+b

The intersection with the Y-axis is obtained by replacing x with 0

The intersection with the X-axis is obtained by replacing y with 0

If we want that the Y-intercept = -5, then

-5 = m(0)+b

So b = -5

Our temporal equation is then

y = mx-5

If we want that the X-intercept = 7, then

0 = m(7)-5

7m = 5

m = 5/7

So our final equation is

$y=\frac{5}{7}x-5$

Attached is the graph of the line

3 0

3 years ago

Which table represents the graph of a logarithmic function in the form y=log3x when b>1?

alex41 [277]

Answer:

The satisfied table of the given function $y = log_{b} (x)$

x 1/8 1/4 1/2 1 2

y -3 -2 -1 0 1

Step-by-step explanation:

Explanation :-

Given logarithmic function $y = log_{b} (x)$ if b >1

Given first table

put x = $\frac{1}{8}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{8} )$

$y = log_{2} (2^{-3} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3$

y = -3

ii)

put x = $\frac{1}{4}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{4} )$

$y = log_{2} (2^{-2} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2$

y = -2

iii)

put x = $\frac{1}{2}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{2} )$

$y = log_{2} (2^{-1} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1$

y = -1

iv)

put x = 1 given b > 1 so we can choose b = 2

$y = log_{2} (1 )$ = 0

y = 0

v)

put x = $2$ given b > 1 so we can choose b = 2

$y = log_{2} (2 )$

y = 1

Final answer:-

The satisfied table of the given function

x 1/8 1/4 1/2 1 2

y -3 -2 -1 0 1

8 0

3 years ago

Read 2 more answers