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Rewrite the following in the form
log(c).

log(2)+log(4)

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

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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 $\log(c)$ . $\newline$ $3 \times \log(2) = \log(2^3) = \log(8)$

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