How do you solve: 3^(x/3) = 5^(x+3) using logs?

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Answer 1 · 2016-04-30T18:01:52

x=-3.88

If #3^(x/3)=5^((x+3))#

if we take logs (I've used natural logs)
#(x/3)*log_e3=(x+3)*log_e5#

#x*log_e3=(3x+9)*log_e5#

#x*log_e3-3x*log_e5=9*log_e5#

#x*(log_e3-3*log_e5)=9*log_e5#

#x*(log_e3-log_e5^3)=9*log_e5#

#x*(log_e3-log_e125)=9*log_e5#

#x*log_e(3/125)=9*log_e5#

#x=9*log_e5/(log_e(3/125))=-3.88#