The movement of the progress bor may be uneven because questions can be worth more or less (including zero) depending on your ons? Use the values log128approx 2.1 and log4approx 0.6 to find the approximate value of log_(4)128 log_(4)128approx underline ( ) The solution is square

To find the approximate value of $log_{4}128$, we can use the change of base formula for logarithms. The change of base formula states that for any positive numbers $a$, $b$, and $c$ (where $a \neq 1$ and $b \neq 1$), the following equation holds:<br /><br />$log_{b}a = \frac{log_{c}a}{log_{c}b}$<br /><br />In this case, we want to find $log_{4}128$, so we can rewrite it as:<br /><br />$log_{4}128 = \frac{log_{10}128}{log_{10}4}$<br /><br />Now, we can use the given values $log128\approx 2.1$ and $log4\approx 0.6$ to substitute into the equation:<br /><br />$log_{4}128 \approx \frac{2.1}{0.6}$<br /><br />Simplifying the fraction, we get:<br /><br />$log_{4}128 \approx 3.5$<br /><br />Therefore, the approximate value of $log_{4}128$ is $\boxed{3.5}$.