How do you solve #3(5)^(2x−3) = 6#?

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Answer 1 · 2018-04-03T21:49:06

#x=ln(250)/ln(25)#

Isolate the exponential #5^(2x-3)# by dividing both sides by #3,# yielding

#5^(2x-3)=2#

Furthermore, recall that #x^(a-b)=x^a/x^b,# so #5^(2x-3)=5^(2x)/5^3=5^(2x)/125#

#5^(2x)/125=2#

#5^(2x)=250#

Now, apply the natural logarithm to both sides.

#ln(5^(2x))=ln(250)#

Recall that #ln(a^b)=blna,# so #ln(5^(2x))=2xln(5)#

#2xln(5)=ln(250)#

Now, solve for #x. # This will be much simpler now as it is not in an exponent or logarithm.

#2x=ln(250)/ln(5)#

#x=ln(250)/(2ln5)#

#x=ln(250)/ln(25)# as #2ln5=ln(5^2)=ln(25)#