The process of simplifying logarithmic expressions requires a strong understanding and application of the logarithmic rules. These encompass the product rule, quotient rule, and power rule, among others. The primary objective here is to break down complicated expressions into more easily understood and manageable forms, thereby facilitating easier computation and clearer comprehension of mathematical theories.
| Topic | Problem | Solution |
|---|---|---|
| None | te the expression as a single logarithm. \[ \frac… | Given the expression \(\frac{1}{3} \ln (x+2)^{3}+\frac{1}{2}\left[\ln (x)-\ln \left(x^{2}+3 x+2\rig… |
| None | Write the expression as a single logarithm with c… | Given the expression \(4 \log _{c} x-6 \log _{c} y^{5}\) |
| None | Write the expression as a single logarithm with c… | Given the expression \(-\frac{2}{3} \log _{6} 6 m^{2}+\frac{1}{2} \log _{6} 36 m^{2}\), we need to … |
| None | Use the properties of logarithms to rewrite the e… | Given the expression \(\log _{m} \sqrt{\frac{5 r^{5}}{z^{7}}}\) |
| None | Condense the following expression by using the pr… | We are given the expression \(4 \log x+6 \log y-10 \log z^{2}\). |
| None | Write the expression as a single logarithm. \[ 7 … | Given the expression \(7 \log _{c}(7 x+1)+\frac{1}{2} \log _{c}(x+8)\) |
| None | Write the expression as a single logarithm. \[ \f… | Given the expression \(\frac{1}{5} \log _{8} z+6 \log _{8} x-\log _{8} y\) |
| None | Write the expression as a single logarithm. \[ 2\… | The given expression is \(2\left(\log _{4} w-4 \log _{4} y\right)+2 \log _{4} z\) |
| None | The equation \[ \ln (x+1)-\ln (x)=2 \] has the so… | Rewrite the equation using the properties of logarithms: \(\ln\left(\frac{x+1}{x}\right) = 2\) |
| None | Solve for $x$ without using a calculating utility… | Rewrite the equation using the properties of logarithms: \(\ln \left(\frac{7}{x} * 8x^3\right) = \l… |