Question

Question 7 Solve 3 log6 2 + 2 log6 3 - log6 x= 2

Answer 1

`3\log _62+2\log _63-\log _6x=2`

Bring up the coefficients as exponents:

`\log _62^3+\log _63^2-\log _6x=2`

Apply product rule of log and quotient rule:

`\log _6((2^3*3^2)/x)=2`
`\log _{6\text{ }}((8*9)/x)=2`
`\log _{6\text{ }}(72)/(x)=2`

If log6 (72/x) = 2, then 72/x= 6^2

`72/x=6^2`
`72/x=36`
`72/36\text{ = x}`
`x=2`