solve 9^x > 54. round to the nearest thousandth.

Answer 1

log9^x =xlog9 > log54

x = log54/log9 = 1.732/0.954 =1.815

9^1.815 = 54

9^1 = 9

9^2 = 81

54 is closer to 81 than 9, so x is closer to 2 than to 1

54 is 5/7 of the way from 9 to 81, so x is about 5/7 of the way from 1 to 2, or 1 5/7 = 1.71 which is close to the actual solution of 1.81, within one decimal place

Answer 2

9^x > 54

Use logs to get the x out of the exponent. You can use any base log. I'll use log base 10 (written as just log).

log(9^x) > log(54)

Now use the property log(a^b) = b·log(a):

x log(9) > log(54)

x > log(54) / log(9)

Use your calculator to find the answer. Round to the nearest hundredth.

Answer 3

9^x > 54; xln9 > ln54. From here x > ln54/ln9; x > 1.815