Solve the equation 19=30(1.2)𝑥 for 𝑥 using logs.

Answer 1

19 = 30(1.2)^x, solve for x using logs

divide both sides by 30

19/30 = 1.2^x

take logs to the base 1.2 of both sides

log_1.2(19/30) = x, log_ba =c is equivalent to b^c = a

x =exactly log_1.2(19/30)

x= the logarthm to the base 1.2 of 19/30

change the base of the log to natural logs, base e

if only to make it easier to calculate on most handheld calculators

or you could alternatively convert to common logs, as ln and log keys

are on most handheld calculators that aren't too expensive, or

go online to a calculator with log functions

use the log property that log_ba = lna/lnb = loga/logb

x = log_1.2(19/30)

x = ln(19/30)/ln1.2

= about -.456758402/.182321556

x= about - 2.505

check the answer

19 = 30(1.2)^-2.505

19= 30/(1.2)^2.505

19 = 30/1.57888

19=19.0008, close enough

UNLESS you really, but most unlikely, meant 19 =30(1.2)x

then

x = 19/30(1.2) = 19/36

x= 19/36

but no need for logs, if that's the problem