Black Christensen
09/30/2023 · Elementary School
Use properties of logarithms to find the exact value of the expression. Do not use a calculator. \( 7^{\log _{7} 8-\log _{7} 5} \) \( 7^{\log _{7} 8-\log _{7} 5}=\square \) (Type an integer or a simplified fraction.)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( 7^{\log_{7} 8 - \log_{7} 5} \), we can use the properties of logarithms.
First, we apply the property of logarithms that states:
\[
\log_{a} b - \log_{a} c = \log_{a} \left( \frac{b}{c} \right)
\]
Using this property, we can rewrite the exponent:
\[
\log_{7} 8 - \log_{7} 5 = \log_{7} \left( \frac{8}{5} \right)
\]
Now, substituting this back into the original expression gives us:
\[
7^{\log_{7} \left( \frac{8}{5} \right)}
\]
Next, we use the property of exponents and logarithms that states:
\[
a^{\log_{a} b} = b
\]
Applying this property, we have:
\[
7^{\log_{7} \left( \frac{8}{5} \right)} = \frac{8}{5}
\]
Thus, the exact value of the expression \( 7^{\log_{7} 8 - \log_{7} 5} \) is:
\[
\boxed{\frac{8}{5}}
\]
Quick Answer
\( 7^{\log_{7} 8 - \log_{7} 5} = \frac{8}{5} \)
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit