Question

What is the value of b in each equation below? Explain your reasoning.

a) log, 243=5
b) log, 0.001=-3

Answer 1

Explanation:

Using the log rule:
`log_ab=c` is equivalent to
`a^c=b`

a)

`log_b243=5`

`b^5=243`

`b=243^{(1)/(5)}`

`b=3`

b)

`log_b0.001=-3`

`b^(-3)=0.001`

`b=0.001^{-(1)/(3) }`

`b=10`

Answer 2

Explanation:

Factorize 243

243 = 3 * 3 * 3 * 3 * 3 = 3⁵

`log_(b) \ 243 = 5 \\\\ log_(b) \ 3^(5) = 5\\\\ 5*log_(b) \ 3 = 5\\\\\\ So, b = 3`because
`log_(3) \ 3 = 1`

b = 3

`b)0.001 = 10^(-3)\\\\ log_(b) \ 0.001 = -3\\\\ log_(b) \ 10^(-3)=-3\\\\ -3*log_(b) \ 10 = -3\\\\ So, b = 10`