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1 year ago

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Explain how to solve 5^(x-2)=8 using log base b of y equals log y over log b. include the solution for x in your answer. round y

our answer to the nearest thousandth.

1 answer:

miskamm [114]1 year ago

5 0

The value of x will be equal to 2.477.

<h3>What is a logarithm?</h3>

The logarithm is the inverse function of exponentiation in mathematics. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.

The given expression will be solved as follows;-

$5^{x-2}= 8$

Taking Log on both sides.

$Log_e 5^{x-2}=Log_e8$

(x-2) Log5 = Log 8

( x-2) = Log8 / Log 5

(x - 2) = Log 8 - Log 5

(x - 2 ) = Log 3

x-2 = 0.477

x = 2.477

Therefore the value of x will be equal to 2.477.

To know more about Logarithm follow

brainly.com/question/25710806

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Use the triangle below to find cos V.

Semenov [28]

Answer:

$cos\ V = \frac{2\sqrt{29}}{29}$

Step-by-step explanation:

Given

The attached triangle

Required

Find cos V

In trigonometry:

$cos\theta = \frac{Adjacent}{Hypotenuse}$

In this case:

$cos V= \frac{TV}{UV}$

Where

$TV = 6$

and

$UV^2 = TV^2 + TU^2$ -- Pythagoras

$UV^2 = 6^2 + 15^2$

$UV^2 = 261$

Take square roots

$UV = \sqrt{261$

$UV = \sqrt{9*29$

$UV = \sqrt{9} *\sqrt{29$

$UV = 3\sqrt{29$

So:

$cos V= \frac{TV}{UV}$

$cos\ V = \frac{6}{3\sqrt{29}}$

$cos\ V = \frac{2}{\sqrt{29}}$

Rationalize:

$cos\ V = \frac{2}{\sqrt{29}}*\frac{\sqrt{29}}{\sqrt{29}}$

$cos\ V = \frac{2\sqrt{29}}{29}$

8 0

2 years ago

A storm moves at a rate of 8 miles per hour. It is 200 miles away from Freeport and headed directly for this town. The equation

Eduardwww [97]

Pls see answer below.

Step-by-step explanation:

In this case, our slope is -8. This means that every hour, the storm is getting closer to the town by 8 miles per hour.

Our y-intercept is 200, which means that its' initial position is 200 miles away from the town.

Hope this helped.

7 0

2 years ago

If the measure of DEF is 65 what is the measure of DE. PLEASE HELP FAST

Wittaler [7]

EF is tangent to the circle we'll assume; otherwise there's no progress.

Call the center C. ECD is isosceles, formed from two radii and the chord.

Angle CED is complementary to DEF

CED = 90 - 65 = 25 degrees

CDE is congruent, isosceles triangle and all that: CDE=25

That leaves DCE=180-25-25=130 degrees

That's the measure of arc DE as well:

Answer: 130 degrees, choice A

8 0

3 years ago

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The floor of a drawing room consists of 2000 tiles. Each of the tiles is rectangular in

wlad13 [49]

Step-by-step explanation:

<h2><u>☼︎</u><u>Given :</u></h2>

The floor of a drawing room consist of 2000 tiles .Each tiles is rectangular in shape , of dimensions ,30 cm × 20 cm.

$\rule{200pt}{3pt}$

<h2><u>☼︎</u><u>To Find :</u></h2>

Area of the room.

$\rule{200pt}{3pt}$

<h2><u>☼︎</u><u>Solution :</u></h2>

<u>~ Formula </u><u>U</u><u>s</u><u>e</u><u>d</u><u>:</u>

$\large{\blue{\bigstar}} \: \: {\underline{\boxed{\pink{\sf{ Area{\small_{(Rectangle)}} = Length \times Breadth }}}}} \: \: {\blue{\bigstar}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

<u>~ Calculating the</u><u> Area of Tiles </u>

${➙ \: {\sf{ Area = Length \times Breadth}}}$

${➙ \: {\sf{ Area = 30 \times 20 }}}$

${\sf{➙ \: Area \: of \: 1 Tiles = {\purple{\bf{ 600 \: cm² }}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

<u>~ Calculating Area of the </u><u>Drawing Room :</u>

${➙ \: {\sf{ Area \: of \: Room \: = No. \: of \: Tiles \times Area \: of \: 1 \: Tile }}}$

${➙ \: {\sf{ Area \: of \: Room \: = 2000 \times 600 }}}$

${\qquad{\sf{ Area \: of \: Room \: = {\color{darkblue}{\bf{ 1200000 \: cm² }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

<u>~ Therefore :</u>

❝ Area of the Drawing room is 1200000 cm² or 12000 m² . ❞

$\begin{gathered} \\ {\blue{\underline{\red{\rule{300pt}{9pt}}}}}\end{gathered}$

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3 years ago

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Simplify: (g^6)(g^11)

11Alexandr11 [23.1K]

Multiplying exponents with like bases is the same as adding up the exponents.
<span>(g^6)(g^11)=g^17

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4 0

2 years ago