Rewrite the following in the form log(c). log(2)+log(4)

Simplifying the expression: log(2) + log(4) Which property can be used to simplify the expression? Sum of logarithms of two numbers equals the logarithm of their product. Product property: log_b P + log_b Q = log_b (PQ)Applying the product property: log(2) + log(4) Apply the product property of logarithms. log(2) + log(4) = log(2 * 4) = log(8)Expressing 8 as a power of 2: Express 8 as a power of 2 in log(8). 8 is 2 cubed, which means 8 = 2^3. log(8) = log(2^3)Applying the power property: log(2^3) Apply the power property of logarithm. Power property of logarithm: log_b P^Q = Q * log_b P log(2^3) = 3 * log(2)Evaluating 3 * log(2): Evaluate 3 * log(2). Since log(2) is just a constant value, multiplying it by 3 does not change the form of the expression, and it remains log(c). 3 * log(2) = log(2^3) = log(8)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Rewrite the following in the form
log(c).

log(2)+log(4)

Rewrite the following in the form $\log (c)$ . $\newline$ $\log (2)+\log (4)$

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate logarithms using properties

Full solution

Q. Rewrite the following in the form

\log (c)

\newline

\log (2)+\log (4)

Simplifying the expression: $\log(2) + \log(4)$ $\newline$ Which property can be used to simplify the expression? $\newline$ Sum of logarithms of two numbers equals the logarithm of their product. $\newline$ Product property: $\log_b P + \log_b Q = \log_b (PQ)$
Applying the product property: $\log(2) + \log(4)$ $\newline$ Apply the product property of logarithms. $\newline$ $\log(2) + \log(4) = \log(2 \times 4) = \log(8)$
Expressing $8$ as a power of $2$ : Express $8$ as a power of $2$ in $\log(8)$ . $\newline$ $8$ is $2$ cubed, which means $8 = 2^3$ . $\newline$ $\log(8) = \log(2^3)$
Applying the power property: $\log(2^3)$ $\newline$ Apply the power property of logarithm. $\newline$ Power property of logarithm: $\log_b P^Q = Q \cdot \log_b P$ $\newline$ $\log(2^3) = 3 \cdot \log(2)$
Evaluating $3 \times \log(2)$ : Evaluate $3 \times \log(2)$ . $\newline$ Since $\log(2)$ is just a constant value, multiplying it by $3$ does not change the form of the expression, and it remains $\log(c)$ . $\newline$ $3 \times \log(2) = \log(2^3) = \log(8)$