15^2x = 36
You’re right – logarithms are the way to go.
Take the log (base 10) of both sides of this equation. From now on, I’ll just write log, but I’ll always refer to log(base 10).
log(15^(2x)) = log(36)
A fundamental rule of logarithms states that for any base b and any real number c and any positive real number a:
log(a^c) = c*log(a)
So log(15^(2x)) = 2x * log(15)……Now we have:
2x * log(15) = log(36)………..dividing both sides by log(15)
2x = log(36) / log(15)
There are some cute tricks to use here, but I’ll use my calculator.
2x = 1.55630 / 1.17609 = 1.32328
By dividing both sides of this equation by 2, we get the final result:
x = 0.6616…..<<<<<.....Answer (rounded to the nearest ten thousandth) --------------------- - - Note when I had 2x = log(36) / log(15), I could have used log(36) = log(6^2) = 2*log(6) and thus got: 2x = 2 * ( log(6) ) / log(15) x = log(6) / log(15) but why bother? . Source(s): 5 years of teaching experience
Apply the newspaper on both sides, we have
log(15^(2x) )=log 36
By the log property we have
2x log 15 = log 36
2x = log 36 / log 15
x= log 36/ (2 log 15)
15^2x = 36
2x log 15 = log 36
2x=log36/log15
x= [log 36/ log 15]/of them
apply log on both sides and it becomes:
2x log(15) = log(36)
connect the journal to the calculator:
2x(1.176) = 1.556
2.352x = 1.556
x = about 0.66
logbase15(36) =2x
log(36)/log(15)= 2x
log(36)/log(15)= 1.32
2x=1.32
1.32/2=0.66