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The exponential form is a way of expressing an equation involving a logarithm as an exponential equation. Logarithms and exponents are intertwined concepts. If you understand one, you can understand the other.
In logarithmic notation, \(\log_{b}(a) = c\) reads as "the logarithm of \(a\) with base \(b\) equals \(c\)."
An equivalent expression in exponential form is \(b^{c} = a\). This means when you see a logarithmic equation, think of what power you need to raise the base to get the number inside the log.
For example, from the logarithmic equation \(\log(7n - 11) = 1\), written in base 10, the exponential form becomes \(10^1 = 7n - 11\). This equation expresses the relationship that 10 raised to the power of 1 equals \(7n - 11\).
By converting the logarithmic equation into an exponential form, solving for the unknown becomes a straightforward arithmetic task.

Solving equations involves finding the value of the unknown that satisfies the equation. Once an equation is in exponential form, it becomes a matter of simple arithmetic to find the unknown variable.
In our example, once we got the exponential form \(10^1 = 7n - 11\), solving for \(n\) starts with isolating \(n\) on one side.
We simplify by adding 11 to both sides of the equation: \[10 + 11 = 7n\]
Which simplifies to: \[21 = 7n\]
Next, we divide both sides by 7 to completely isolate \(n\):
\[n = \frac{21}{7}\]
This results in \(n = 3\).
Rely on these steps, ensuring every operation is performed equally on both sides of the equation, keeping the equation balanced, and zeroing in on the unknown.

Logarithmic properties are key to understanding how logarithms simplify complex operations. They can make equations easier to solve.
There are several basic properties of logarithms to be aware of:

• Product Property: \(\log_b(xy) = \log_b(x) + \log_b(y)\)
• Quotient Property: \(\log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y)\)
• Power Property: \(\log_b(x^n) = n \cdot \log_b(x)\)
• Change of Base Formula: \(\log_b(x) = \frac{\log_k(x)}{\log_k(b)}\), where \(k\) is any positive number

Each property can be applied in solving various logarithmic equations by simplifying the equation.
In the solved exercise, the implicit understanding that \(\log(7n - 11) = 1\) uses base 10 leverages these properties inadvertently. Having these properties at your fingertips challenges more complex logarithmic equations, making them less daunting.