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3 years ago

If log a = x and log b = y, then log (ab2) equals

Mathematics

1 answer:

mylen [45]3 years ago

3 0

Answer:

The answer for log(ab²) is x + 2y.

Step-by-step explanation:

You have to apply Logarithm Law,

$log(a) + log(b) \: ⇒ \: log(a \times b)$

$log( {a}^{n} ) \: ⇒ \: n log(a)$

In this question, you have to seperate it out :

$log(a {b}^{2} ) = log(a) + log( {b}^{2} )$

$log( {b}^{2} ) = 2 log(b)$

$let \: log(a) = x$

$let log(b) = y$

$log(a {b}^{2} ) = log(a) + 2 log(b)$

$log(a {b}^{2} ) = x + 2y$

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In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=29°, and JH = 88 feet. Find the length of IJ to the nearest tenth of a foot.

Nitella [24]

We have been given that in ΔHIJ, the measure of ∠J=90°, the measure of ∠I=29°, and JH = 88 feet. We are asked to find the length of IJ to the nearest tenth of a foot.

First of all, we will draw a right triangle using our given information as shown in the attachment.

We can see that in triangle HIJ, the side IJ is adjacent side to angle I and JH is opposite side to angle I.

We know that tangent relates opposite side of right triangle to adjacent side.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(29^{\circ})=\frac{88}{IJ}$

$IJ=\frac{88}{\text{tan}(29^{\circ})}$

$IJ=\frac{88}{0.554309051453}$

$IJ=158.7562024638191237$

Upon rounding to nearest tenth, we will get:

$IJ\approx 158.8$

Therefore, the length of the side IJ is approximately 258.8 units.

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4 years ago

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A ladder is leaning against a wall that is 20 ft tall. The base of the ladder is 30 ft from the wall. How long is the ladder?

creativ13 [48]

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4 years ago

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Ted borrowed $100 from 2 years at a 10% interest rate. How much interest will he pay on the loan? What will be the total amount

mr_godi [17]

Answer:

Interest = $20

Amount due = $120

Step-by-step explanation:

This is a Simple Interest problem. Simple interest is given as:

I = (P * R * T) / 100

Where I = interest

P = principal or amount loaned

R = rate of interest

T = time elapsed

Ted borrowed $100 from 2 years at a 10% interest rate.

This means that P = $100, R = 10%, T = 2 years.

Hence, the interest will be:

I = (100 * 10 * 2) / 100

I = 2000 / 100

I = $20

The interest after two years will be $20.

Therefore, the total amount due at the end of the loan is:

A = P + I

A = 100 + 20 = $120

The amount due is $120.

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4 years ago

Kareem stepped to the free throw line for two shots. if the probability of making each shot is 3/4,what is the probability that

EastWind [94]

To calculate the probability of making both shots you will multiply the probability of making .one by the same probability.

3/4 x 3/4 = 9/16

The probability of Kareem making both shots is 9/16.

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4 years ago

WICH EQUATION CAN BE USED TO FIND THE AREA OF THE RECTANGLE

allsm [11]

Answer:

A = L x W

Step-by-step explanation:

<em>Because the equation of a rectangle is understood the best way to help you understand the equation of l*w is to break down the definiton of a rectangle.</em>

Defining a rectangle:

The rectangle is a quadrillateral with two parallel sets of sides which are perpendicular to each other.

Understanding it:

Now let's look at a rectangle

Let's say the length is 5 units and the width is 10 units.

To find that meat in between we understand that 5 units of length extends through all 10 units of the width. This means 5 is carried out for 10 units meaning that 5x10 is the area of the Rectangle. As such the area would be 50

So the area of a rectangle is its length times its width

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3 years ago