Question

how do I solve this: Use log4^2=0.5 , log4^3≈0.7925 , and log4^5≈1.1610 to approximate the value of the given expression. Enter your answer to four decimal places. log420

Answer 1

The expression given is log4^x, and we are asked to approximate the value of this expression to four decimal places. To do this, we can use the three given values to interpolate a value for x.

Using the three given values, we can set up a logarithmic equation as follows:

log4^2=0.5

log4^3≈0.7925

log4^5≈1.1610

Solving for x, we get x≈4.1222. Therefore, the approximate value of the given expression to four decimal places is log4^4.1222 ≈ 1.0206.