When solving for x as an exponent, we need to use logarithms in order to undo the operation and rearrange the terms. We use log rules to bring down the exponent and solve. Logarithms are the inverse operations to exponents and vice versa. We have one special kind of logarithm called the natural logarithm whose base is e. We write it as ln. Since our base is e here, we will use the natural logarithm to rearrange and isolate x.

$e^{4x-1} =3$

We begin by applying the natural logarithm to each side.

$ln(e^{4x-1}) =ln(3)$

Log rules allow use to rearrange the exponent as multiplication in front of the log.

$(4x-1)ln(e) =ln(3)$

ln e as an inverse simplifies to 1.

$(4x-1)(1)=ln(3)$

We now apply the inverse operations for subtraction and multiplication.

$4x-1+1=1+ln(3)\\4x=1+ln(3)\\\frac{4x}{4} =\frac{1+ln3}{4} \\x =\frac{1+ln3}{4}$

Option A is correct.

5 0

3 years ago

Which of the following sets of inequalities

Ludmilka [50]

Inequalities help us to compare two unequal expressions. The correct options are 2 and 3.

<h3>What are inequalities?</h3>

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The inequality for the red portion is,

slope, m = (-2/-4) = 1/2

y-intercept is 2.

y ≤ (1/2)x + 2

The inequality for the blue portion is,
slope, m = (5-0)/(3-0.5) = 2

y-intercept is -1.

y > 2x - 1

Hence, the correct options are 2 and 3.

Learn more about Inequality:

brainly.com/question/19491153

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7 0

1 year ago

4. Ten less than the product of six and eight less than a number

ICE Princess25 [194]

Answer: 38

Step-by-step explanation:

6 x 8 = 48

48 - 10 = 38

7 0

3 years ago