Please help.

What is the solution to the equation below? riund your answer to two decimal places. (24) log(3x) = 60

Amanda [17]

The answer is: " x = 105.41 " .

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Explanation:

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Given: " 24 log (3x) = 60 " ; Solve for "x" .

The default is to assume "base 10" for the "logarithm".

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Start by dividing each side of the equation by "24" ;

→ [ 24 log(3x) ] / 24 = 60 / 24 ;

to get:

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log (3x) = 2.5 ;

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Rewrite as: log₁₀ (3x) = 2.5 ;

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Using the property of logarithms:

⇔ 10⁽²·⁵⁾ = 3x ;

↔ 3x = 10⁽²·⁵⁾ ;

→ 10^ (2.5) = 316.2277660168379332 ;

→ 3x = 316.227766016837933 ;

Divide each side of the equation by "3" ;

to isolate "x" on one side of the equation;

and to solve for "x" ;

→ 3x / 3 = 316.2277660168379332 / 3 ;

to get:

→ x = 105.4092553389459777333 ;

→ round to 2 (two) decimal places;

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→ " x = 105.41 " .

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Hope this helps!

Best wishes to you!

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8 0

3 years ago

Help me plz, explain it

Darya [45]

The perimeter of a rectangle is found by multiplying the length by 2 and the width by 2 and adding them together.

P = 2L + 2W

Filling in the information given we can find the width:

16.8 = 2(3.6) + 2W

16.8 = 7.2 + 2W

2w = 16.8 - 7.2

2w = 9.6

w = 9.6 / 2

w = 4.8 in.

6 0

3 years ago

Read 2 more answers

Use the distributive property to find the product of 7 × 14.6.<br> 98.6<br> 102.2<br> 21.6<br> 98.42

umka2103 [35]

Answer:

98.42

Step-by-step explanation:

7 × 14.6 =

= 7 × (7 + 7 + 0.6)

= 7 × 7 + 7 × 7 + 7 × 0.6

= 49 + 49 = 0.42

= 98.42

5 0

2 years ago

What is the volume of a rectangular prism with length 8 cm, height 4 cm, and width 7 cm?

Bogdan [553]

Volume = Area * height
= width * length * height
= 8 * 4 * 7
= 224 cm^3

4 0

3 years ago

Galena is solving the following system. 3x+2y+3z =5 7x+y +7z=-1 4x-4y-z=-3

babymother [125]

Answer:

She did not multiply equation 3 in step 2 by the correct value.

Step-by-step explanation:

Given:

$3x+2y+3z=5\\7x+y+7z=-1\\4x-4y-z=-3$

In order to solve this, we need to eliminate any one variable and then form a simultaneous equation with the remaining two variables. Then, we nee to solve the simultaneous equation.

Here, Galena is trying to eliminate the variable $z$ first.

Step 1: She multiplies equation (3) by 3 and adds it to equation (1)

Let us multiply equation (3) by 3

$(4x-4y-z=-3)\times 3 = (3\times 4x)-(3\times 4y)-(3\times z)=3\times -3\\(4x-4y-z=-3)\times 3 =12x-12y-3z=-9$

Now, adding this to equation 1 will cancel out z terms.

$12x-12y-3z+3x+2y+3z=-9+5\\(12x+3x)+(-12y+2y)+(3z-3z)=-4\\15x-10y+0=-4$

Now, she need to make one more equation in $x\ and \ y$ .

Step 2: She multiplies equation (3) by -7 and adds it to equation (2)

Multiplying equation (3) by -7 will give,

$(4x-4y-z=-3)\times -7 = (-7\times 4x)-(-7\times 4y)-(-7\times z)=-7\times -3\\(4x-4y-z=-3)\times 3 =-28x+28y+7z=21$

Now, adding this to equation 2 will not cancel out z terms.

$-28x+28y+7z+7x+y+7z=21-1\\(-28x+7x)+(28y+y)+(7z+7z)=20\\-21x+29y+14z=20$

So, she makes mistake in step 2 as the $z$ terms are not being cancelled.

6 0

3 years ago

Read 2 more answers