Question

assume \\(\log_{b}x = 0.53\\). evaluate \\(\log_{b}x^{2}\\) \\(\log_{b}x^{2}=\square\\) (type an integer or a decimal.)

Explanation:

Step1: Recall the power rule of logarithms

The power rule of logarithms states that $\log_b a^n = n\log_b a$.

Step2: Apply the power rule to $\log_b x^2$

Using the power rule, we have $\log_b x^2 = 2\log_b x$.

Step3: Substitute the given value of $\log_b x$

We know that $\log_b x = 0.53$, so substitute this into the expression: $2\times0.53 = 1.06$.

Answer:

1.06