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3 years ago

Rewrite the equation in logarithmic form: 2³= 8

Mathematics

2 answers:

elena55 [62]3 years ago

7 0

Answer:

3 log 2 = log 8

Step-by-step explanation:

Take the log of both sides of the given equation 2^3 = 8:

log 2^3 = log 8, which simplifies to 3 log 2 = log 8.

This is equivalent to the given 2^3 = 8.

Instead of the common log, you could also use the natural log, "ln."

Alternatively, use the base-2 log:

2^3 = 8

Taking the base-2 log of both sides, we get 3 = log-2 of 8 = 3

GrogVix [38]3 years ago

6 0

Explanation: The base of the power in the original equation becomes the base of the log. So we have $^{log}2$ . Next, the exponent in the original equation goes on the other side of the equation and finally, the result in the original equation goes inside the log.

So we have $^{log} 2$ $8$ = $3$ which is 2³ = 8 written in logarithmic form.

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Find the lengths and slopes of the diagonals to name the parallelogram. Choose the most specific name. E (-2, -4), F(0, -1), G(-

Kay [80]

Answer:

1) d) Square

2) Proofs that PWRS is a rhombus are

Length of QS ≠ PR and

Slope of segment QR and PS is -1/2 and Slope of segment RS and QP is -2.

Step-by-step explanation:

The given points (x, y) of the parallelogram are;

E(-2, -4), F(0, -1), G(-3, 1), H(-5, -2)

The slope, m, of the segments are found as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

By computation, the slope of segment EF = 1.5

The slope of segment FG = -0.67

The slope of segment GH = 1.5

The slope of segment HE = -0.67

Therefore, EF is parallel to GH and FG is parallel to HE

The length of the sides are;

$\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

By computation, the length of segment EF = 3.61

The length of segment FG = 3.61

The length of segment GH = 3.61

The length of segment HE = 3.61

The diagonals are;

EG and FH

The length of segment EG = 5.099

The length of segment FH = 5.099

Therefore, the diagonals are equal and the parallelogram is a square

2) The given dimensions are;

P(-1, 3), Q(-2, 5), R(0, 4), S(1, 2)

A rhombus has all sides equal

The length of segment PQ = 2.24

The length of segment QR = 2.24

The length of segment RS = 2.24

The length of segment PS = 2.24

The diagonals are;

QS and PR

The length of segment QS = 4.24

The length of segment PR = 1.41

The slope of segment QR = -0.5

The slope of segment PS = -0.5

The slope of segment RS = -2

The slope of segment QP = -2

Therefore, QS≠QR the parallelogram is a rhombus

The correct option ;

Length of QS ≠ PR and

Slope of segment QR and PS is -1/2 and Slope of segment RS and QP is -2.

Where there are acute angles in parallelogram PQRS, then the correct option is d) Length of QR and PS is 2.2 and Length of RS and QP is 2.2

8 0

3 years ago

Mrs perry shares out 28 biscuits between Gemma and Zak in the ratio 1:6

dsp73

One of them will be given 4 biscuits and the other will be given 24.

5 0

3 years ago

A mixture of alcohol and water contains a total of 60 oz of liquid there are 12 oz of pure alcohol in the mixture was a percenta

OlgaM077 [116]

Answer:

The mixture contains 80% water and 20% alcohol.

Step-by-step explanation:

Given:

Total Amount of mixture = 60 oz

Amount of alcohol in the mixture = 12 oz

We need to find the percentage of water and percentage of alcohol in the mixture.

Solution:

First we will find the amount of water in mixture.

Now we know that;

Total Amount of mixture is equal to sum of Amount of alcohol in the mixture and amount of water in mixture.

so we can say that;

amount of water in mixture = Total Amount of mixture - Amount of alcohol in the mixture

amount of water in mixture = $60-12 =48\ oz$

Now we will find the Percentage amount of water.

Percentage amount of water can be calculated by dividing amount of water in mixture by Total Amount of mixture and then multiplying by 100.

framing in equation form we get;

Percentage amount of water = $\frac{48}{60}\times 100 = 80\%$

Percentage amount of alcohol = $100\%-80\%=20\%$

Hence The mixture contains 80% water and 20% alcohol.

7 0

3 years ago

2x−8=20 steps to solving

Art [367]

Add 8 to both sides
2x = 28
Divide 2 to both sides
Solution: x = 14

4 0

2 years ago

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A. Going 20 miles per hour over the speed limit will result in a fine of $ 2

Zina [86]

Assuming that the cost of the fine is proportionate per each 20mph increase, then a 40mph speeding ticket should be $4, and if they received a fine of $150 would be a crazy amount of speed, is there something you did not attach?

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3 years ago