Question

Write the expression as a single logarithm. 5logby + 6 log b x

Answer 1

Logb ((y^5)(x^6)) is the answer

Answer 2

The given expression
`5log_(b)y+6log_(b) x` can be written as a single logarithm as
`log_(b)(y^5x^6)`

Explanation:

Consider the given expression,

`5log_(b)y+6log_(b)x`

Using the property of logarithm,
`log_ax^n=nlog_ax`

Applying reverse of above property, given expression becomes,

`5log_(b)y+6log_(b)x`

`\Rightarrow log_(b)y^5+log_(b)x^6` ...(1)

Now again using the property of logarithm
`log_(a)xy=log_ax+log_ay`

(1) can be written as,

`log_(b)y^5+log_(b)x^6`

`\Rightarrow log_(b)(y^5x^6)`

Thus, the given expression
`5log_(b)y+6log_(b) x` can be written as a single logarithm as
`log_(b)(y^5x^6)`