Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $w$ . $\newline$ $9^w = 81$ $\newline$ $w$ = ____

View step-by-step help

View step-by-step help

Solve equations with variable exponents

Full solution

Q. Solve for

w

.

\newline

9^w = 81

\newline

w

= ____

Recognize relationship: Step $1$ : Recognize the relationship between the base and the result. $\newline$ $9^w = 81$ . $\newline$ We know that $81$ is a power of $9$ .
Express as power: Step $2$ : Express $81$ as a power of $9$ . $\newline$ $81 = 9^2$ . $\newline$ So, $9^w = 9^2$ .
Set exponents equal: Step $3$ : Since the bases are the same, set the exponents equal to each other. $w = 2$ .

More problems from Solve equations with variable exponents

Question

Write the expression using an exponent.

\newline

2 \times 2

\newline

Posted 2 months ago

Question

Evaluate the expression.

4 - 4^2

Posted 2 months ago

Question

x^2 = 4

Posted 1 month ago

Question

x^2 = 9

Posted 3 months ago

Question

\newline

x^2 = 0

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

Posted 3 months ago

Question

x

\newline

8 = 2^x

\newline

x =

Posted 3 months ago

Question

x

\newline

6 = 7^x

\newline

x =

Posted 3 months ago

Question

Select the equivalent expression.

\newline

((8^{-5})/(2^{-2}))^{-4}=?

\newline

1

\newline

\newline

(8^{20})/(2^{8})

\newline

\newline

(2^{6})/(8^{9})

\newline

\newline

(1)/(8\cdot 2^{2})

Posted 4 days ago

Question

Select the equivalent expression.

\newline

\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?

\newline

1

\newline

\frac{b^{21}}{4^{15}}

\newline

\frac{4^{15}}{b^{21}}

\newline

b^{-21}\cdot 4^{-15}

Posted 1 month ago

Question

Select the equivalent expression.

\newline

(3^{3}\cdot6^{6})^{-3}=

\newline

1

\newline

\frac{1}{3^{9}\cdot6^{18}}

\newline

\frac{6^{18}}{3^{9}}

\newline

\frac{3^{9}}{6^{18}}

Posted 1 month ago