Question

Given log(d)=1, evaluate the following logarithm: log_(d)((7)/(6))

Answer 1

The value of
`log_(d) (7/6)` is
`0.15415067982725836.`

Step-by-step explanation:

To evaluate the logarithm
`log_(d) (7/6)`, we can use the change-of-base formula:

`log_(a) (b)` =
`log_c(b)/log_c(a)`

Setting
`a = d` and
`b = (7/6)`, we can rewrite the given logarithm as:

`log_(d) (7/6)` =
`log_(c) (7/6) /log_c(d)`

Since we are given that
`log(d) = 1`, we can substitute this value into the above equation to get:

`log_(d) (7/6)` =
`log_c(7/6)`/1

Now, we need to choose a base c that will make the logarithm on the left-hand side of the equation easier to evaluate. One common choice is to use the base e (the natural logarithm base), which has some nice properties that make it convenient for calculations.

Setting c = e, we get:

`log_(d) (7/6)` =
`log_e(7/6)/1`

Using the definition of the natural logarithm, we know that
`log_e(7/6)` =
`ln(7/6)` . Therefore, we can rewrite the above equation as:

`log_(d) (7/6)` =
`ln(7/6)/1`

Finally, we can evaluate the natural logarithm using a calculator to get:

`log_(d) (7/6)` =
`ln(7/6)` =
`0.15415067982725836`

Therefore, the value of the logarithm
`log_(d) (7/6)` is
`0.15415067982725836.`