Subjects algebra

Log Base 3 4148A8

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1. The problem asks us to find the expression when the base of the logarithm is changed to 3. 2. Recall the change of base formula for logarithms: $$\log_b a = \frac{\log_c a}{\log_c b}$$ where $c$ is any positive number different from 1. 3. If we want to express $\log_3 x$ in terms of common logarithms (base 10) or natural logarithms (base $e$), we use: $$\log_3 x = \frac{\log x}{\log 3}$$ 4. This means that if the original logarithm had a different base, we can convert it to base 3 by dividing the logarithm of the argument by the logarithm of 3. 5. For example, if the original expression was $\log_b x$, then changing the base to 3 gives: $$\log_3 x = \frac{\log_b x}{\log_b 3}$$ 6. This formula allows us to rewrite logarithms with any base into logarithms with base 3. 7. This is useful because sometimes calculations or simplifications are easier with a specific base. Final answer: $$\log_3 x = \frac{\log x}{\log 3}$$