Question Prompt: Question prompt: What is the value of log(10 × sqrt(x - 3))?Understand the Problem: Understand the problem. We need to evaluate the expression log(10 × sqrt(x - 3)). This is a logarithmic expression, and we cannot simplify it further without knowing the value of x. However, we can express it in a simpler logarithmic form using logarithmic properties.Apply Logarithmic Property: Apply the logarithmic property of the product. The logarithm of a product is equal to the sum of the logarithms of the individual factors. Therefore, we can write log(10 × sqrt(x - 3)) as log(10) + log(sqrt(x - 3)).Simplify First Term: Simplify the first term. Since log(10) is a common logarithm (base 10), and we are taking the log of the base itself, log(10) simplifies to 1.Apply Square Root Property: Apply the logarithmic property of the square root. The square root can be written as an exponent of 1/2. Therefore, log(sqrt(x - 3)) can be written as log((x - 3)^(1/2)).Apply Exponent Property: Apply the logarithmic property of exponents. The logarithm of a power is equal to the exponent times the logarithm of the base. Therefore, log((x - 3)^(1/2)) can be written as (1/2) * log(x - 3).Combine Simplified Terms: Combine the simplified terms. Now we combine the results from Step 3 and Step 5 to get the final simplified expression: 1 + (1/2) * log(x - 3).

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\log(10 \times\sqrt{x-3})$

View step-by-step help

Home

Math Problems

Precalculus

Properties of logarithms: mixed review

Full solution

\log(10 \times\sqrt{x-3})

Question Prompt: Question prompt: What is the value of $\log(10 \times \sqrt{x - 3})$ ?
Understand the Problem: Understand the problem. $\newline$ We need to evaluate the expression $\log(10 \times \sqrt{x - 3})$ . This is a logarithmic expression, and we cannot simplify it further without knowing the value of $x$ . However, we can express it in a simpler logarithmic form using logarithmic properties.
Apply Logarithmic Property: Apply the logarithmic property of the product. $\newline$ The logarithm of a product is equal to the sum of the logarithms of the individual factors. Therefore, we can write $\log(10 \times \sqrt{x - 3})$ as $\log(10) + \log(\sqrt{x - 3})$ .
Simplify First Term: Simplify the first term. $\newline$ Since $\log(10)$ is a common logarithm (base $10$ ), and we are taking the log of the base itself, $\log(10)$ simplifies to $1$ .
Apply Square Root Property: Apply the logarithmic property of the square root. The square root can be written as an exponent of $\frac{1}{2}$ . Therefore, $\log(\sqrt{x - 3})$ can be written as $\log((x - 3)^{\frac{1}{2}})$ .
Apply Exponent Property: Apply the logarithmic property of exponents. $\newline$ The logarithm of a power is equal to the exponent times the logarithm of the base. Therefore, $\log((x - 3)^{\frac{1}{2}})$ can be written as $\frac{1}{2} \cdot \log(x - 3)$ .
Combine Simplified Terms: Combine the simplified terms. $\newline$ Now we combine the results from Step $3$ and Step $5$ to get the final simplified expression: $1 + (\frac{1}{2}) \cdot \log(x - 3)$ .