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2 years ago

11

Use natural logarithms to solve the equation. Round to the nearest thousandth. 7e3x − 4 = 14

1 answer:

dusya [7]2 years ago

5 0

Answer:

0.315 to nearest thousandth.

Step-by-step explanation:

7e^3x − 4 = 14

7e3x = 18

e^3x = 18/7

3x = ln(18/7)

x = ln(18/7) / 3

= 0.31482.

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For what value of x is sq 896z^15/225z^6 = xz^4/15

Ratling [72]

Answer:

Value of x is, 8

Step-by-step explanation:

Given: $\sqrt{\frac{896z^{15}}{225z^6}} =\frac{xz^4}{15} \sqrt{14z}$ ,.....[1]

To find the value of x:

Using exponent rules:

$(a^n)^m = a^{nm}$

$a^n \cdot a^m = a^{n+m}$

Taking square both sides in [1] we have;

$\frac{896z^{15}}{225z^6} = (\frac{xz^4}{15})^2 \cdot (14z)$

Simplify:

$\frac{896z^{15}}{225z^6} =\frac{x^2z^8}{225} \cdot (14z)$

or

$\frac{896z^{15}}{225z^6} =\frac{14x^2z^9}{225}$

Multiply both sides by $\frac{225}{14z^9}$ we get;

$x^2 = \frac{896 z^{15}}{225z^6} \times \frac{225}{14 z^9} = \frac{896 z^{15}}{14 z^{9+6}}$

Simplify:

$x^2 = \frac{896 z^{15}}{14 z^{15}} = 64$

or

$x = \sqrt{64}$

Simplify:

x = 8

Therefore, the value of x is, 8

5 0

2 years ago

Is y=4x+3 a one step or a two step problem

Hunter-Best [27]

Answer:

y=4x-3

then add 3 to each side to get: y+3=4x.

Next, just divide both sides by 4 to get x = (y+3)\div4.

3 0

2 years ago

Read 2 more answers

On a map, the distance from Akron to Cleveland measures 2 centimeters. What is the actual distance if the scale of the map shows

WINSTONCH [101]

To answer this question you will set up the proportion shown in the attached picture.

There are 2 ways to solve this.

1. You can create an equivalent ratio by determining the factor that will take you from 1 cm to 2 cm and apply his factor to the 19 miles.

The answer would be 19 x 2= 38 miles for 2 centimeters.

2. The second strategy is to use cross products to get an answer. You multiply the number diagonal from each other. See picture for this work.

4 0

3 years ago

Solve the following equations.<br> log2(x^2 − 16) − log^2(x − 4) = 1

Alenkasestr [34]

Answer:

$x=\frac{4*(2+e)}{e-2}$

Step-by-step explanation:

Let's rewrite the left side keeping in mind the next propierties:

$log(\frac{1}{x} )=-log(x)$

$log(x*y)=log(x)+log(y)$

Therefore:

$log(2*(x^{2} -16))+log(\frac{1}{(x-4)^{2} })=1\\ log(\frac{2*(x^{2} -16)}{(x-4)^{2}})=1$

Now, cancel logarithms by taking exp of both sides:

$e^{log(\frac{2*(x^{2} -16)}{(x-4)^{2}})} =e^{1} \\\frac{2*(x^{2} -16)}{(x-4)^{2}}=e$

Multiply both sides by $(x-4)^{2}$ and using distributive propierty:

$2x^{2} -32=16e-8ex+ex^{2}$

Substract $16e-8ex+ex^{2}$ from both sides and factoring:

$-(x-4)*(-8-4e-2x+ex)=0$

Multiply both sides by -1:

$(x-4)*(-8-4e-2x+ex)=0$

Split into two equations:

$x-4=0\hspace{3}or\hspace{3}-8-4e-2x+ex=0$

Solving for $x-4=0$

Add 4 to both sides:

$x=4$

Solving for $-8-4e-2x+ex=0$

Collect in terms of x and add $4e+8$ to both sides:

$x(e-2)=4e+8$

Divide both sides by e-2:

$x=\frac{4*(2+e)}{e-2}$

The solutions are:

$x=4\hspace{3}or\hspace{3}x=\frac{4*(2+e)}{e-2}$

If we evaluate x=4 in the original equation:

$log(0)-log(0)=1$

This is an absurd because log (x) is undefined for $x\leq 0$

If we evaluate $x=\frac{4*(2+e)}{e-2}$ in the original equation:

$log(2*((\frac{4e+8}{e-2})^2-16))-log((\frac{4e+8}{e-2}-4)^2)=1$

Which is correct, therefore the solution is:

$x=\frac{4*(2+e)}{e-2}$

6 0

3 years ago

Marnie practiced her basketball dribbling. After two tries she had bounced the ball 88 times. On the second try she had 2 fewer

wolverine [178]

44

88 * 2 = 44

Your welcome

4 0

3 years ago