I don't understand this problem:
(1/2)n = 0.015625
n log 0.5 = log 0.015625
n = log 0.5 / log 0.015625
n = 6
When I plug log .5 into the calculator it gives .3010 and when I plug .15625 to the calculator it is -1.806 and that would be -.3010/-1.806 =.1666. How is the answer 6? Really, can you provide a detailed explanation? I am really confused.
It's because you should have divide by log .5:
n = log 0.015625 / log .5
Note that .16667 = 1/6, the reciprocal of the answer.
<ouch> slap forehead! </ouch>
Sure! Let's go through the problem step by step to understand it better.
First, let's address the calculation of log(0.5) and log(0.015625):
- The value of log(0.5) is approximately 0.3010. The base of the logarithm is usually assumed to be 10 unless specified otherwise.
- The value of log(0.015625) is approximately -1.806.
Now let's look at the equation and solve for 'n':
(1/2)n = 0.015625
To solve for 'n', we can take the logarithm of both sides of the equation:
log((1/2)n) = log(0.015625)
Using the property of logarithms, we can bring down the exponent n:
n * log(1/2) = log(0.015625)
Now, substitute the values we obtained earlier for log(1/2) and log(0.015625):
n * 0.3010 = -1.806
To isolate 'n', divide both sides of the equation by 0.3010:
n = -1.806 / 0.3010
After evaluating the division, we find:
n ≈ -6
It seems there may have been an error in the calculation you mentioned earlier. The value of n should be approximately -6, not 6.
Please double-check your calculations and make sure to input the correct values into the calculator.
To understand the problem, let's walk through it step by step:
Step 1: Start with the equation (1/2)n = 0.015625.
Step 2: To solve for n, we want to isolate n on one side of the equation. Divide both sides by (1/2):
(1/2)n / (1/2) = 0.015625 / (1/2)
n = 0.015625 / (1/2)
n = 0.015625 * 2
n = 0.03125
Now, let's analyze where you might have made a mistake:
In the step where you wrote n log 0.5 = log 0.015625, you misunderstood the concept of logarithms. The equation should be written as n * log(0.5) = log(0.015625).
Step 3: To find the value of n, divide both sides by log(0.5):
n * log(0.5) / log(0.5) = log(0.015625) / log(0.5)
n = log(0.015625) / log(0.5)
Here, you correctly wrote the equation as n = log(0.015625) / log(0.5).
Step 4: Now, let's evaluate the expression using a calculator to find the value of n:
n = log(0.015625) / log(0.5)
n ≈ -4.0 / -0.3010
n ≈ 13.289
After evaluating the expression, we find that the value of n is approximately equal to 13.289, not 6.
It seems there was an error in your calculation. Double-check the values you input into the calculator for log(0.5) and log(0.015625). These values should be approximately -0.3010 and -4.0, respectively.
Therefore, the correct value of n is approximately 13.289, not 6.