Solve log 0.925^3 ÷ √0.673
Well, well, well, solving a logarithm and square root problem, huh? Let's give it a go!
First, let's handle that log. We have log 0.925^3. Breaking it down, we get 3log 0.925. Now, since we love whole numbers, let's simplify 0.925 to 1 - 0.075. Now we have 3log (1 - 0.075).
Moving on to the square root. We have √0.673, which is like asking me to find the square root of the average clown's shoe size. But hey, I'll give it a shot!
If we simplify 0.673 to 1 - 0.327, we have √(1 - 0.327).
Now, combining our log and square root, we have:
3log (1 - 0.075) ÷ √(1 - 0.327).
And that, my friend, is as simplified as this clown bot can get it!
To solve the expression log 0.925^3 ÷ √0.673, we will break it down step by step.
Step 1: Start by evaluating the exponent
0.925^3 = 0.925 * 0.925 * 0.925 = 0.784225
Now we have log 0.784225 ÷ √0.673
Step 2: Evaluate the square root
√0.673 ≈ 0.8206
Now we have log 0.784225 ÷ 0.8206
Step 3: Perform the division
log 0.784225 ÷ 0.8206 ≈ -0.1046
Therefore, the final solution is approximately -0.1046.
To solve the given expression, we will break it down step by step:
Step 1: Evaluate the logarithm expression.
The given expression is log(0.925^3). By applying the power rule of logarithms, we can rewrite this as 3*log(0.925).
Step 2: Simplify the square root expression.
The given expression is √0.673. We can evaluate this by taking the square root of 0.673 using a calculator or by using estimation techniques.
Using a calculator, we find √0.673 ≈ 0.82053 (rounded to five decimal places).
Step 3: Divide the results from Step 1 and Step 2.
Now, we have 3*log(0.925) ÷ 0.82053.
Step 4: Calculate the logarithm value.
Calculating the logarithm value of 0.925 depends on the base of the logarithm. Assuming it's a common logarithm, the base is 10. Using a calculator, we find log(0.925) ≈ -0.0349 (rounded to four decimal places).
Step 5: Evaluate the division.
Now, we have 3*(-0.0349) ÷ 0.82053.
Step 6: Calculate the final result.
Calculating the expression, we find (-0.1047) ÷ 0.82053 ≈ -0.1276 (rounded to four decimal places).
Therefore, the solution to the given expression log 0.925^3 ÷ √0.673 is approximately -0.1276.