Question

If you're good at logarithms please help me with question j on the bottom

Answer 1

`\log _x\left(6\right)`

`$\frac{\text{log}(6)}{\text{log}(x)} =\frac{\text{log}(3)}{\text{log}x)}+\frac{\text{log}(3)}{\text{log}(x)}=\frac{1.5}{\text{log}(x)}+\frac{1.5}{\text{log}(x)}=(3)/(\log _(10)\left(x\right))$`

Answer 2

Explanation:

`a) \\ log_(x)(15) \\ = log_(x)(3 * 5) \\ = log_(x)3 + log_(x)5 \\ = 1.5 + 1.8 \\ = 3.3`

`b) \\ log_(x)(2) \\ = log_(x)((10)/(5)) \\ = log_(x)10 - log_(x)5 \\ = 3 - 1.8\\</p><p>= 1.2`

`e) \\ log_(x)(150) \\ = log_(x)(3 * 5* 10) \\ = log_(x)3 + log_(x)5+ log_(x)10 \\ = 1.5 + 1.8 + 3\\ = 6.3`

`f) \\ log_(x)(250) \\ = log_(x)( 5^2 * 10) \\ = log_(x)5^2 + log_(x)10 \\ </p><p>= 2log_(x)5 + log_(x)10 \\ </p><p></p><p> = 2* 1.8 + 3\\ </p><p>= 3.6 + 3\\</p><p></p><p>= 6.6`