Use the change of base formula to approximate the solution to log0.515 = 1 – 2x. Round to the nearest hundredth.

Guest Jun 9, 2015

#1**+10 **

I'm not sure that the change of base formula would do much good here, since we're already using base 10....here's my approach...

log0.515 = 1 – 2x and we can write

log0.515 = log 10 - 2x rearrange

2x = log 10 - log0.515

2x = log (10/0.515) divide both sides by 2

x = log(10/0.515)/ 2 ≈ 1.288 ≈ 1.29 to the nearest hundredth

CPhill
Jun 10, 2015

#1**+10 **

Best Answer

I'm not sure that the change of base formula would do much good here, since we're already using base 10....here's my approach...

log0.515 = 1 – 2x and we can write

log0.515 = log 10 - 2x rearrange

2x = log 10 - log0.515

2x = log (10/0.515) divide both sides by 2

x = log(10/0.515)/ 2 ≈ 1.288 ≈ 1.29 to the nearest hundredth

CPhill
Jun 10, 2015