fieldlandman said:when trying to solve
ln(x+4)=2
i tried this
ln(x+4)=2
e^2=(x+4)
A natural logarithm, or ln, is the inverse function of the exponential function. It is used to find the time needed to reach a certain level of growth, or to find the time when an initial value will reach a certain final value when continuously growing at a certain rate.
Natural logs are used to solve exponential growth or decay problems, as well as to model many real-world situations such as population growth, radioactive decay, and interest rates. They allow us to easily convert between exponential and logarithmic equations.
To solve a natural log equation, isolate the ln term on one side of the equation and exponentiate both sides using e (Euler's number). Then, solve for the variable using algebraic techniques such as factoring or the quadratic formula.
The main difference between ln and log is the base of the logarithm. ln uses e as its base, while log typically uses base 10. This means that ln is more frequently used in scientific and mathematical contexts, while log is more commonly used in financial and business contexts.
Some common mistakes when solving natural log equations include not isolating the ln term, forgetting to exponentiate both sides, and not simplifying the resulting equation enough. It is also important to check for extraneous solutions, as natural logs do not allow for negative arguments.