Evaluate Log10 (13/3) + log10 (186/65) - log10 (31/25)
Evaluate Log10 (13/3) + log10 (186/65) - log10 (31/25)= 1
Using logarithmic rules, we can simplify the expression as follows:
log10 (13/3) + log10 (186/65) - log10 (31/25)
= log10 [(13/3) x (186/65) / (31/25)] (using the rule that log (A) + log (B) = log (A x B) and log (A) - log (B) = log (A/B))
= log10 [(13 x 186 x 25) / (3 x 65 x 31)]
= log10 [(13 x 5) / (3 x 31)]
= log10 (65/93)
If log10 (65/93) = 1, then we can write:
10^1 = 65/93
Multiplying both sides by 93, we have:
10^1 x 93 = 65
Thus, the value of the expression is 1 if log10 (13/3) + log10 (186/65) - log10 (31/25) = 1 and we have 65 as one possible solution.
AAAaannndd the bot gets it wrong yet again!
log10 (13/3) + log10 (186/65) - log10 (31/25)
= log10(13/3 * 186/65 * 25/31)
= log10((13*186*25)/(3*65*31))
= log10(60450/6045)
= log10(10)
= 1
Apologies for my earlier mistake. You are correct. Here is the correct solution:
log10 (13/3) + log10 (186/65) - log10 (31/25)
= log10(13/3 * 186/65 * 25/31)
= log10((13*186*25)/(3*65*31))
= log10(60450/6045)
= log10(10)
= 1
Thank you for bringing this to my attention.
To evaluate the expression Log10(13/3) + Log10(186/65) - Log10(31/25), we can use the following steps:
Step 1: Simplify the logarithmic expressions by applying the properties of logarithms.
For the first term, Log10(13/3), we can simplify it using the division property of logarithms:
Log10(13/3) = Log10(13) - Log10(3)
Similarly, for the second term, Log10(186/65), we have:
Log10(186/65) = Log10(186) - Log10(65)
For the third term, Log10(31/25), we have:
Log10(31/25) = Log10(31) - Log10(25)
Step 2: Substitute the simplified expressions back into the original expression.
Log10(13) - Log10(3) + Log10(186) - Log10(65) - Log10(31) + Log10(25)
Step 3: Apply the properties of logarithms to further simplify the expression.
Use the subtraction property of logarithms to combine terms with the same base (Log10):
Log10(13) + Log10(186) + Log10(25) - (Log10(3) + Log10(65) + Log10(31))
Step 4: Use the properties of logarithms to combine and simplify the terms.
Take the logarithm of each number:
Log10(13) ≈ 1.1139
Log10(186) ≈ 2.2695
Log10(25) ≈ 1.3979
Log10(3) ≈ 0.4771
Log10(65) ≈ 1.8129
Log10(31) ≈ 1.4914
Substitute the values back into the expression:
1.1139 + 2.2695 + 1.3979 - 0.4771 - 1.8129 + 1.4914
Step 5: Add or subtract the terms to get the final result.
1.1139 + 2.2695 + 1.3979 - 0.4771 - 1.8129 + 1.4914 ≈ 4.9837
Therefore, Log10(13/3) + Log10(186/65) - Log10(31/25) is approximately equal to 4.9837.
Using logarithmic rules, we can simplify the expression as follows:
log10 (13/3) + log10 (186/65) - log10 (31/25)
= log10 [(13/3) x (186/65) / (31/25)] (using the rule that log (A) + log (B) = log (A x B) and log (A) - log (B) = log (A/B))
= log10 [(13 x 186 x 25) / (3 x 65 x 31)]
= log10 [(13 x 5) / (3 x 31)]
= log10 (65/93)
Therefore, the final answer is log10 (65/93).