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3 years ago

Solve the following logarithmic equations. 5 log(x + 4) = 10

Mathematics

1 answer:

Ede4ka [16]3 years ago

6 0

Answer:

$x=e^{2} -4$

Step-by-step explanation:

Divide both sides by 5:

$log(x+4)=\frac{10}{5} \\log(x+4)=2$

Cancel logarithms by taking exp of both sides:

$e^{log(x+4)}=e^{2} \\x+4=e^{2}$

Solve for x subtracting 4 from both sides:

$x=e^{2} -4$

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2 years ago

Find a solution to the linear equation −2x−2y=8 by filling in the boxes with a valid value of x and y.Provide your answer below:

inna [77]

Given

$-2x-2y=8$

To find a solution for the linear equation, the first step is to write the equation in slope-intercept form:

-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of the equal sign:

$\begin{gathered} -2x+2x-2y=8+2x \\ -2y=2x+8 \end{gathered}$

-Divide both sides by -2:

$\begin{gathered} \frac{-2y}{-2}=\frac{2x}{-2}+\frac{8}{-2} \\ y=-x-4 \end{gathered}$

Once you have expressed the equation of the line in slope-intercept form, replace it with any value for x and calculate the corresponding value of y, for example, x=2

$\begin{gathered} y=-(2)-4 \\ y=-2-4 \\ y=-6 \end{gathered}$

One solution for the linear equation is x=2 and y=-6, you can check the solution by replacing the values on the original equation, with both values the result should be 8:

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1 year ago