Question

Use the change of base formula to find log14, 18. Round to the nearest hundredth.​

Answer 1

To find log14 18 using the change of base formula, we can use the natural logarithm as the new base. The approximate value of log14 18 is 1.096.

Step-by-step explanation:

To use the change of base formula to find log14 18, we can use either the common logarithm (base 10) or the natural logarithm (base e) as our new base. Let's use the natural logarithm.

The change of base formula states that loga x = logb x / logb a, where a is the original base, x is the number being evaluated, and b is the new base.

So, log14 18 = loge 18 / loge 14. Using a calculator, we find that loge 18 ≈ 2.8904 and loge 14 ≈ 2.6391, therefore, log14 18 ≈ 2.8904 / 2.6391 ≈ 1.096.

Answer 2

Solution of the expression is 1.07

Step-by-step explanation:

The given logarithmic expression is
`log_(14)18`

Since change of base formula says,
`log_(b)(a)=(log_(10)(a))/(log_(10)(b))`

Therefore, the given expression can written as
`(log_(10)(18))/(log_(10)14)` by using change of base formula.

Now
`(log_(10)(18))/(log_(10)(14))=(1.2253)/(1.1461)`

= 1.069

≈ 1.07

Therefore, solution of the expression will be 1.07