Use the change of base formula log 6 basee 50 what you discovered to calculate the value of rounding to thousandths.

Answer 1

log₆50

Using the change of base formula would be

log 50/log 6 = 2.1833

Answer 2

log6 base 50

= ln6/ln50

= about 0.45801353

= about .458

log50 base 6 = ln50/ln6 = 1/.458 = 2.183

logs base b = lns/lnb = logs/logb = log s to any base a/log b to any base a

Answer 3

Problem

Given the logarithm log₆(50), use the change-of-base formula to calculate its approximate value to three decimal places.

Step 1

Recall that the change-of-base formula for logarithms is:

log_b(a) = (log_x(a)) / (log_x(b))

In this case, we will use x = 10 because most scientific calculators only support base-10 and natural (base-e) logarithms. However, this means that x = e will also work here.

Step 2

Apply the formula using the logarithm given in the problem:

log₆(50) = log₁₀(50) / log₁₀(6) or ln(50) / ln(6)

Step 3

Plug in the results obtained from step 2 into a calculator:

TI-84 Plus: 2.183341611...

Desmos: 2.183341610...

Solution

log₆(50) ≈ 2.183.

Answer 4

To calculate log⁡6(50)\log_6(50) using the change of base formula, we can use the following formula:

log⁡b(a)=log⁡c(a)log⁡c(b)\log_b(a) = \frac{\log_c(a)}{\log_c(b)}Where:

1. bb is the original base (6 in this case),
2. aa is the argument (50 in this case),
3. cc is the new base (we'll use base ee or natural logarithm, which is denoted as ln⁡\ln).

Step 1: Apply the Change of Base Formula

We can write:

log⁡6(50)=ln⁡(50)ln⁡(6)\log_6(50) = \frac{\ln(50)}{\ln(6)}Step 2: Calculate the Natural Logarithms

We need to calculate the natural logarithms of 50 and 6:

1. ln⁡(50)≈3.912\ln(50) \approx 3.912
2. ln⁡(6)≈1.792\ln(6) \approx 1.792

Step 3: Divide the Results

Now, divide the two results to get log⁡6(50)\log_6(50):

log⁡6(50)=3.9121.792≈2.18\log_6(50) = \frac{3.912}{1.792} \approx 2.18Final Answer:

Thus, log⁡6(50)≈2.18\log_6(50) \approx 2.18 (rounded to the thousandths place).

Answer 5

See the videa.