Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the exponential equation for
x.

56^(3x-8)=1

x=

Solve the exponential equation for $x$ . $\newline$ $56^{3 x-8}=1$ $\newline$ $x=$

View step-by-step help

View step-by-step help

Solve exponential equations by rewriting the base

Full solution

Q. Solve the exponential equation for

x

.

\newline

56^{3 x-8}=1

\newline

x=

Write as power term: Write $1$ as a power term with $56$ as the base. $\newline$ Any natural number raised to the power of $0$ is $1$ . $\newline$ So, $1 = 56^0$
Set exponent equal to $0$ : Set the exponent of the base $56$ in the equation equal to $0$ . Since $56^{3x-8} = 56^0$ , we can equate the exponents because the bases are the same. $3x - 8 = 0$
Solve for x: Solve for x. $\newline$ Add $8$ to both sides of the equation to isolate the term with $x$ . $\newline$ $3x - 8 + 8 = 0 + 8$ $\newline$ $3x = 8$
Divide by $3$ : Divide both sides by $3$ to solve for $x$ . $x = \frac{8}{3}$

More problems from Solve exponential equations by rewriting the base

Question

x

\newline

5^x=1

\newline

\newline

Write your answer in simplest form.

Posted 5 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.

Posted 4 months ago

Question

Use the following function rule to find

f(1)

\newline

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

Posted 5 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 8 months ago

Question

x

\newline

7 = 9^x

\newline

Round your answer to the nearest thousandth.

Posted 4 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 7 months ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 9 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 7 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 4 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) = 6x

\newline

f(x) = 6^x

\newline

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

\newline

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

Posted 4 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant