Question

Given that

log 2= X
log 3= y
log 7= z
Express the following expressions in terms of x, y, and z

(1) log (14/3)
(2) log 0.3
(3) log 10.5

Answer 1

Answer: See below

Explanation:

Answer (1)

We must break down the expressions into factors. That is:

`\begin{align} \log 12&=\log 4* 3=\log 2^2* 3\\ \log 12&=\log 2^2+\log 3=2\log 2+\log 3=2x+y\\ \end{align}`
`\log (14)/(3)&=\log 14-\log 3 \\ =\log 2* 7-\log 3\\ \\\log (14)/(3)& =\log 2+\log 7-\log 3 \\ =x+z-y\\`

Answer (2)

`\log 0.3 &=\log (3)/(10) \\ \\ =\log 3-\log 10 \\=y-1`

Answer (3)

`\log 10.5& \\ =\log (21)/(2) \\=\log 21-\log 2\\ \\ \log 10.5& \\ =\log 3* 7-\log 2\\=\log 3+\log 7-\log 2\\=y+z-x`