Evaluate log of 9

Problem

(log_)(9)

Solution

1. Identify the base of the logarithm. In most mathematical contexts, (log_)(x) without a specified base refers to the common logarithm (base 10), though in higher mathematics it can refer to the natural logarithm (base e. Assuming the common logarithm: (log_10)(9)

2. Rewrite the argument as a power. Since 9=3 the expression becomes (log_10)(3)

3. Apply the power rule for logarithms, which states (log_b)(xp)=p*(log_b)(x) This gives 2*(log_10)(3)

4. Substitute the approximate value of (log_10)(3) which is approximately 0.4771

5. Calculate the final numerical value: 2×0.4771=0.9542

Final Answer

(log_)(9)≈0.9542

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