Similarly, for the third term, (𝑚−𝑥)log⁡(1−𝑝)(m−x)log(1−p), we use the chain rule with 𝑢=1−𝑝u=1−p. The derivative of log⁡(1−𝑝)log(1−p) with respect to 1−𝑝1−p is 11−𝑝1−p1​ . Multiplying by −(𝑚−𝑥)−(m−x) (due to the chain rule) gives −𝑚−𝑥1−𝑝− 1−pm−x​ .

If 𝑚log⁡32+2log⁡3𝑚=m log 3​ 2 +2 log 3​ m = 2, then what is the value of 𝑚m ?

Use the rules of logarithms to write the following expression in terms of ln(𝑥) and ln(𝑦).ln(𝑥3𝑦)=

log 3​ (m 4 )=log 3​ (3 12 )

The expression loge(4e3x)log𝑒⁡(4𝑒3𝑥) is equal to

se the rules of logarithms to write the following expression in terms of ln(𝑥) and ln(𝑦).ln(𝑥3𝑦)=