Log 3-(log4+5)= 18

To solve the equation \( \log 3 - (\log 4 + 5) = 18 \), we can start by simplifying the left side of the equation. 1. Rewrite the equation: \[ \log 3 - \log 4 - 5 = 18 \] 2. Combine the logarithmic terms: \[ \log 3 - \log 4 = \log\left(\frac{3}{4}\right) \] Therefore, we can rewrite the equation as: \[ \log\left(\frac{3}{4}\right) - 5 = 18 \] 3. Add 5 to both sides: \[ \log\left(\frac{3}{4}\right) = 18 + 5 \] \[ \log\left(\frac{3}{4}\right) = 23 \] 4. Convert the logarithmic equation to its exponential form. If \( \log_a(b) = c \), then \( b = a^c \). Here, we assume the logarithm is base 10: \[ \frac{3}{4} = 10^{23} \] 5. This is a contradiction because \( \frac{3}{4} \) is a small number less than 1, while \( 10^{23} \) is a very large number. Therefore, the equation has no solutions. In conclusion, the equation \( \log 3 - (\log 4 + 5) = 18 \) has no valid solution.