Question

Please help. Write as a single logarithm, a) log(13)+log(4) b) log(small 5)(14)-log(small 5)(2)

Answer 1

a)
`\log 52`

b)
`\log_57`

Explanation:

Use logarithm properties:

`\log_ab+\log_ac=\log_a(b\cdot c)\\ \\\log_ab-\log_ac=\log_a(b)/(c)`

Then

a)
`\log 13+\log 4=\log 13\cdot 4=\log 52`

b)
`\log_514-\log _52=\log _5(14)/(2)=\log _57`