Rewrite using power rule: We are given the expression 8log₅(a) + 2log₅(b) and we need to simplify it. According to the properties of logarithms, specifically the power rule which states that m*logₐ(b) = logₐ(b^m), we can rewrite each term by moving the coefficients as exponents inside the logarithms.Apply power rule to first term: Applying the power rule to the first term, we get log₅(a^8).Apply power rule to second term: Applying the power rule to the second term, we get log₅(b^2).Combine using product rule: Now we have the expression log₅(a^8) + log₅(b^2). According to the properties of logarithms, specifically the product rule which states that logₐ(x) + logₐ(y) = logₐ(xy), we can combine these two logarithms into a single logarithm.Final simplified expression: Combining the two logarithms using the product rule gives us log₅(a^8 * b^2).The expression log₅(a^8 * b^2) is the simplified form of the original expression 8log₅(a) + 2log₅(b).

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$2$ ) $8 \log _{5} a+2 \log _{5} b$

View step-by-step help

Home

Math Problems

Algebra 1

Domain and range of square root functions: equations

Full solution

2

)

8 \log _{5} a+2 \log _{5} b

Rewrite using power rule: We are given the expression $8\log_5(a) + 2\log_5(b)$ and we need to simplify it. According to the properties of logarithms, specifically the power rule which states that $m\log_a(b) = \log_a(b^m)$ , we can rewrite each term by moving the coefficients as exponents inside the logarithms.
Apply power rule to first term: Applying the power rule to the first term, we get $\log_5(a^8)$ .
Apply power rule to second term: Applying the power rule to the second term, we get $\log_5(b^2)$ .
Combine using product rule: Now we have the expression $\log_5(a^8) + \log_5(b^2)$ . According to the properties of logarithms, specifically the product rule which states that $\log_a(x) + \log_a(y) = \log_a(xy)$ , we can combine these two logarithms into a single logarithm.
Final simplified expression: Combining the two logarithms using the product rule gives us $\log_5(a^8 \cdot b^2)$ .
Final simplified expression: Combining the two logarithms using the product rule gives us $\log_5(a^8 \cdot b^2)$ .The expression $\log_5(a^8 \cdot b^2)$ is the simplified form of the original expression $8\log_5(a) + 2\log_5(b)$ .