Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

6*2^((x)/(4))=222
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.

x~~

$6 \cdot 2^{\frac{x}{4}}=222$ $\newline$ What is the solution of the equation? $\newline$ Round your answer, if necessary, to the nearest thousandth. $\newline$ $x \approx$

View step-by-step help

View step-by-step help

Solve exponential equations using common logarithms

Full solution

Q.

6 \cdot 2^{\frac{x}{4}}=222

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

x \approx

Isolate exponential term: Isolate the exponential term. $\newline$ To solve for $x$ , we first need to isolate the term containing the variable $x$ , which is $2^{x/4}$ . We do this by dividing both sides of the equation by $6$ . $\newline$ $6 \cdot 2^{x/4} = 222$ $\newline$ $2^{x/4} = \frac{222}{6}$ $\newline$ $2^{x/4} = 37$
Take logarithm of sides: Take the logarithm of both sides. $\newline$ To solve for the exponent $x/4$ , we take the logarithm of both sides of the equation. We can use the natural logarithm (ln) or the logarithm base $2$ (log $_2$ ) for convenience. Here, we'll use the natural logarithm. $\newline$ $\ln(2^{x/4}) = \ln(37)$
Apply power rule: Apply the power rule of logarithms. $\newline$ The power rule of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . We apply this rule to the left side of the equation. $\newline$ $\frac{x}{4} \cdot \ln(2) = \ln(37)$
Solve for x: Solve for x. $\newline$ Now we need to solve for x by multiplying both sides of the equation by $4$ and then dividing by $\ln(2)$ . $\newline$ $x = \frac{4 \cdot \ln(37)}{\ln(2)}$
Calculate x value: Calculate the value of x. $\newline$ Using a calculator, we find the value of $x$ . $\newline$ $x \approx (4 \times \ln(37)) / \ln(2)$ $\newline$ $x \approx (4 \times 3.610918) / 0.693147$ $\newline$ $x \approx 14.443672 / 0.693147$ $\newline$ $x \approx 20.839$

More problems from Solve exponential equations using common logarithms

Question

Solve. Write your answer as an integer or a fraction in simplest form.

\newline

5^x=1

\newline

x=

Posted 3 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

\newline

\$

Posted 3 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

\newline

f(1) =

Posted 2 months ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = 9^x

\newline

x =

Posted 3 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 2 months ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 3 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 2 months ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 3 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6^x

\newline

f(x) = 6x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 3 months ago