MATH SOLVE

4 months ago

Q:
# what is the true solution to 3 in 2 + in 8 = 2 in (4x)

Accepted Solution

A:

The first step for solving this equation is to determine the defined range.

3㏑(2) + ㏑(8) = 2㏑(4x), x > 0

Write the number 8 in exponential form.

3㏑(2) + ㏑(2³) = 2㏑(4x)

Using ㏑([tex] a^{x} [/tex]) = x × ㏑(a),, transform the expression.

3㏑(2) + 3㏑(2) = 2㏑(4x)

Now collect the like terms on the left side of the equation.

6㏑(2) = 2㏑(4x)

Switch the sides of the equation.

2㏑(4x) = 6㏑(2)

Using x × ㏑(a) = ㏑([tex] a^{x} [/tex]),, transform the expression on the left side of the equation.

㏑((4x)²) = 6㏑(2)

Using x × ㏑(a) = ㏑([tex] a^{x} [/tex]),, transform the expression on the right side of the equation.

㏑((4x)²) = ㏑([tex] 2^{6} [/tex])

Since the bases of the logarithms are the same,, you need to set the arguments equal.

(4x)² = [tex] 2^{6} [/tex]

Take the square root of both sides of the equation and remember to use both the positive and negative roots.

4x = +/- 8

Now separate the equation into 2 possible cases.

4x = 8

4x = -8

Solve the top equation for x.

x = 2

Solve the bottom equation for x.

x = 2

, x > 0

x = -2

Lastly,, check if the solution is in the defined range to find your final answer.

x = 2

This means that the correct answer to your question is x = 2.

Let me know if you have any further questions

:)

3㏑(2) + ㏑(8) = 2㏑(4x), x > 0

Write the number 8 in exponential form.

3㏑(2) + ㏑(2³) = 2㏑(4x)

Using ㏑([tex] a^{x} [/tex]) = x × ㏑(a),, transform the expression.

3㏑(2) + 3㏑(2) = 2㏑(4x)

Now collect the like terms on the left side of the equation.

6㏑(2) = 2㏑(4x)

Switch the sides of the equation.

2㏑(4x) = 6㏑(2)

Using x × ㏑(a) = ㏑([tex] a^{x} [/tex]),, transform the expression on the left side of the equation.

㏑((4x)²) = 6㏑(2)

Using x × ㏑(a) = ㏑([tex] a^{x} [/tex]),, transform the expression on the right side of the equation.

㏑((4x)²) = ㏑([tex] 2^{6} [/tex])

Since the bases of the logarithms are the same,, you need to set the arguments equal.

(4x)² = [tex] 2^{6} [/tex]

Take the square root of both sides of the equation and remember to use both the positive and negative roots.

4x = +/- 8

Now separate the equation into 2 possible cases.

4x = 8

4x = -8

Solve the top equation for x.

x = 2

Solve the bottom equation for x.

x = 2

, x > 0

x = -2

Lastly,, check if the solution is in the defined range to find your final answer.

x = 2

This means that the correct answer to your question is x = 2.

Let me know if you have any further questions

:)