Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for the exact value of
x.

6ln(4x+9)+4=-14
Answer:

Solve for the exact value of $x$ . $\newline$ $6 \ln (4 x+9)+4=-14$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Solve equations with variables on both sides: fractional coefficients

Full solution

Q. Solve for the exact value of

x

.

\newline

6 \ln (4 x+9)+4=-14

\newline

Answer:

Isolate natural logarithm term: First, we need to isolate the natural logarithm term on one side of the equation. We can do this by subtracting $4$ from both sides of the equation. $\newline$ $6\ln(4x+9) + 4 - 4 = -14 - 4$ $\newline$ $6\ln(4x+9) = -18$
Divide by $6$ : Next, we divide both sides of the equation by $6$ to solve for the natural logarithm of $(4x+9)$ . $\frac{6\ln(4x+9)}{6} = \frac{-18}{6}$ $\ln(4x+9) = -3$
Exponentiate to remove ln: Now, we will exponentiate both sides of the equation to remove the natural logarithm. We use the property that $e^{\ln(x)} = x$ . $\newline$ $e^{\ln(4x+9)} = e^{-3}$ $\newline$ $4x+9 = e^{-3}$
Subtract $9$ : We then subtract $9$ from both sides of the equation to isolate the term with $x$ . $\newline$ $4x+9 - 9 = e^{-3} - 9$ $\newline$ $4x = e^{-3} - 9$
Divide by $4$ : Finally, we divide both sides by $4$ to solve for $x$ . $\frac{4x}{4} = \frac{e^{(-3)} - 9}{4}$ $x = \frac{e^{(-3)} - 9}{4}$

More problems from Solve equations with variables on both sides: fractional coefficients

Question

Write the sentence as an equation.

\newline

138

is equal to the quotient of

w

30

\newline

/

) if you want to use a division sign.

\newline

Posted 3 months ago

Question

\newline

(\frac{2}{7})x= -14

\newline

x =

Posted 4 months ago

Question

(\frac{8}{5})x= 32

Posted 4 months ago

Question

\newline

2+2

\newline

Posted 4 days ago

Question

-27x+18y=54

Posted 4 months ago

Question

\newline

48.5-0.434=

Posted 4 months ago

Question

\newline

96.7-0.163=

Posted 4 months ago

Question

\newline

4.43-0.283=

Posted 4 months ago

Question

\newline

3.05-0.338=

Posted 4 months ago

Question

\newline

6.168-0.432=

Posted 4 months ago