Solved example of exponential equations
We can take out the unknown from the exponent by applying logarithms in base $10$ to both sides of the equation
Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Divide both sides of the equation by $\log \left(3\right)$
Apply the change of base formula for logarithms: $\log_b(a)=\frac{\log_x(a)}{\log_x(b)}$
Decompose $81$ in it's prime factors
Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Decompose $9$ in it's prime factors
Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Evaluating the logarithm of base $3$ of $3$
Multiply $4$ times $1$
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