Question

Simplify the expression without a calculator. Use the properties of logarithms.log6 9 + log6 4 =

Answer 1

We have the next expression

`\log _69+\log _64`

And we must simplify it

1. we must use the next property of logarithms

`\log _b(xy)=\log _bx+\log _by`

In this case,

`\log _69+\log _64=\log _6(9\cdot4)=\log _636`

2. Using the definition of logarithms

`b^a=x\text{ if and only if }\log _bx=a`

In this case,

`\begin{gathered} 6^x=36 \\ \text{then,} \\ x=2 \end{gathered}`

Finally,

`\log _69+\log _64=2`

ANSWER:

`\log _69+\log _64=2`