When it comes to solving logarithms, what you're essentially doing is identifying the exponent that a base must be amplified by to derive a certain number. To illustrate, in the equation log base 2 of 8 equals 3, this signifies that 2, raised to the power of 3, results in 8. It's key to grasp the connection between logarithms and exponents, particularly when working through exponential equations.
| Topic | Problem | Solution |
|---|---|---|
| None | If $\log (x)=-0.123$, what does $x$ equal? Expres… | The question is asking for the value of \(x\) given that \(\log (x)=-0.123\). The logarithm functio… |
| None | Solve the equation $\log (x+22)+\log (x+1)=2$. If… | Combine the two logarithms into one using the property of logarithms that states that the sum of tw… |
| None | Fill in the missing values to make the equations … | Use the logarithm properties to solve these equations. The properties are as follows: |
| None | Solve the equation. Write the solution set with t… | The given equation is in the form of an exponential equation. To solve for t, we can take the logar… |
| None | Use the definition of logarithm to find the missi… | Use the definition of logarithm to find the missing value: \(\log _{b} 144=2\) |
| None | Solve the following logarithmic equation. \[ \fra… | Given the logarithmic equation \(\frac{1}{2} \log _{9} x=3 \log _{9} 5\) |
| None | Solve the logarithmic equation. Be sure to reject… | The given equation is a logarithmic equation. The first step to solve this equation is to combine t… |
| None | Solve for $x$ : \[ \log (x)+\log (x+3)=5 \] \[ x=… | Given the equation \(\log (x)+\log (x+3)=5\) |
| None | This problem uses the Richter scale for the stren… | The problem uses the Richter scale for the strength of an earthquake. The strength, \(W\), of the s… |
| None | Solve for $17^{x}$ if $\log _{3}\left((-26)+17^{x… | First, we rewrite the equation using the property of logarithms, which states that \(\log _{b} a^{n… |
| None | Given that log x=25 and log 25 approx 1.4, evalua… | Given that \(\log x = 25\) and \(\log 25 \approx 1.4\), we need to evaluate the given expression \(… |