Question

Evaluate Log10 (13/3) + log10 (186/65) - log10 (31/25)

Answer 1

Evaluate Log10 (13/3) + log10 (186/65) - log10 (31/25)= 1

Answer 2

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

Answer 3

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).

Answer 4

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.

Answer 5

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.