Solve for x and type your answer as simply as an integer or decimal value. if you can’t type the number exactly, round to 4 decimal digits. if it’s a fractional value, put a 0 in front of the decimal. x: log 3 - 3 log x = 2

Solve this just like you would any equation for x.  Move the log 3 over by the 2 and have -3log x = 2 - log3.  I don't like negatives out in front so i changed all the signs (that's allowed; as long as you change ALL the signs within the expression it remains equal to what it was originally)? 3log x = log3 - 2.  Now divide both sides by 3 and you'll have  .  When you do the math on your calculator for the right side you get that logx= -.5076262484.  Take the inverse of that on your calculator because you're looking for the number that has the log of that negative decimal.  The inverse log of that number gives you that x = .3107.  You could plug it back in to the original equation and see that it works.

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

The answer would be 7 cages