Write the expression below as a single logarithm in simplest form. log_(b)10-log_(b)10 Answer: log_(b)(◻)

Identify Property: Identify the property used to combine the logarithms. The expression given is log_b(10) - log_b(10), which involves the subtraction of two logarithms with the same base. The subtraction of logarithms corresponds to the division of their arguments according to the quotient property of logarithms. Quotient Property: log_b(P) - log_b(Q) = log_b(P/Q)Apply Quotient Property: Apply the quotient property to combine the logarithms. Using the quotient property, we can write the expression as a single logarithm: log_b(10) - log_b(10) = log_b(10/10)Simplify Argument: Simplify the argument of the logarithm. The argument of the logarithm simplifies to: 10/10 = 1 So, the expression becomes log_b(1).Recognize Logarithm Value: Recognize the value of the logarithm of 1. The logarithm of 1 to any base is always 0 because any number raised to the power of 0 is 1. Therefore, log_b(1) = 0.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the expression below as a single logarithm in simplest form.

log_(b)10-log_(b)10
Answer:
log_(b)(◻)

Write the expression below as a single logarithm in simplest form. $\newline$ $\log _{b} 10-\log _{b} 10$ $\newline$ Answer: $\log _{b}(\square)$

View step-by-step help

Home

Math Problems

Algebra 2

Quotient property of logarithms

Full solution

Q. Write the expression below as a single logarithm in simplest form.

\newline

\log _{b} 10-\log _{b} 10

\newline

Answer:

\log _{b}(\square)

Identify Property: Identify the property used to combine the logarithms. $\newline$ The expression given is $\log_b(10) - \log_b(10)$ , which involves the subtraction of two logarithms with the same base. $\newline$ The subtraction of logarithms corresponds to the division of their arguments according to the quotient property of logarithms. $\newline$ Quotient Property: $\log_b(P) - \log_b(Q) = \log_b\left(\frac{P}{Q}\right)$
Apply Quotient Property: Apply the quotient property to combine the logarithms. $\newline$ Using the quotient property, we can write the expression as a single logarithm: $\newline$ $\log_b(10) - \log_b(10) = \log_b(\frac{10}{10})$
Simplify Argument: Simplify the argument of the logarithm. $\newline$ The argument of the logarithm simplifies to: $\newline$ $\frac{10}{10} = 1$ $\newline$ So, the expression becomes $\log_b(1)$ .
Recognize Logarithm Value: Recognize the value of the logarithm of $1$ . The logarithm of $1$ to any base is always $0$ because any number raised to the power of $0$ is $1$ . Therefore, $\log_b(1) = 0$ .