How do you solve 1/2=10^(1.5x)?

2 Answers
Mar 13, 2016

x = -0.200686663

Explanation:

1 / 2 = 10^(1.5 * x)
Take Log on both sides
log (1 / 2) = 1.5 x * log 10
(Hope you are aware of the relationship
log a^x = x * log a)
Now log ( 1 / 2) = log 2^-1 = -1 * log 2
log 2 = 0.3010300 (this you can get from any log tables or calculator)
So, -0.3010300 = 1.5 x
or x = -0.3010300 / 1.5 = -0.200686663
Hope it is clear

Mar 13, 2016

:.x=-2/3log_10 2

Explanation:

tking log_10 on both sides

log_10(1/2)=log_10 10^(1.5x)

=>log_10 1-log_10 2=log_10 10^(1.5x)

=>0-log_10 2=x*1.5xxlog_10 10

=>0-log_10 2=(3x)/2
:.x=-2/3log_10 2