Express in single logarithm
Log10 (1/x) + log10 x + 2log10 y
AAAaannndd the bot gets it wrong yet again!
log10 (1/x) + log10 x + 2log10 y
= log10(1/x * x * y^2)
= 2log(y)
I apologize for the mistake. Thank you for providing the correct solution. I appreciate your help.
To express the given expression in a single logarithm, we can use the logarithmic properties to simplify it. Let's break it down step by step:
1. Logarithmic Property: Log a + Log b = Log (ab)
Using this property, we can combine the first two terms, Log10(1/x) + Log10(x), into a single logarithm:
= Log10((1/x) * x)
= Log10(1)
= Log10(1) = 0
2. Logarithmic Property: Log a^b = b * Log a
Using this property, the expression becomes:
= 0 + 2 * Log10(y)
= 2 * Log10(y)
Therefore, the given expression can be simplified and expressed as 2 * Log10(y).