T thetomps Junior Member Joined Sep 26, 2005 Messages 59 Oct 31, 2005 #1 If ln(x - 10) - ln(x - 4) + ln(x + 11) = ln (x + 3), then x = 49???
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Oct 31, 2005 #2 Hello, thetomps! If ln(x - 10) - ln(x - 4) + ln(x + 11) = ln (x + 3), then x = 49 ? Click to expand... Yes! . . . Nice work! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ You can <u>check</u> your answer, you know . . . Plug \(\displaystyle x = 49\) into the equation. .Is the statement true? We have: . \(\displaystyle \ln(49 - 10)\ -\ \ln(49 - 4)\ +\ \ln(49 + 11) \;\;^?=^? \;\;\ln(49 + 3)\) Then: . \(\displaystyle \ln(39)\ -\ \ln(45)\ +\ \ln(60) \;\;^?=^? \;\;\ln(52)\) The left side is: .\(\displaystyle \ln\left(\frac{39\cdot60}{45}\right) \;= \;\ln\left(\frac{2340}{45}\right) \;= \;\ln(52)\) . . . yay!
Hello, thetomps! If ln(x - 10) - ln(x - 4) + ln(x + 11) = ln (x + 3), then x = 49 ? Click to expand... Yes! . . . Nice work! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ You can <u>check</u> your answer, you know . . . Plug \(\displaystyle x = 49\) into the equation. .Is the statement true? We have: . \(\displaystyle \ln(49 - 10)\ -\ \ln(49 - 4)\ +\ \ln(49 + 11) \;\;^?=^? \;\;\ln(49 + 3)\) Then: . \(\displaystyle \ln(39)\ -\ \ln(45)\ +\ \ln(60) \;\;^?=^? \;\;\ln(52)\) The left side is: .\(\displaystyle \ln\left(\frac{39\cdot60}{45}\right) \;= \;\ln\left(\frac{2340}{45}\right) \;= \;\ln(52)\) . . . yay!
