How do you solve #6.5^x = 8.4^(4x-10)#?

1 Answer
Gió
Mar 4, 2016

I found #x=3.2#

Explanation:

Apply the natural log to both sides:
#ln(6.5)^(x)=ln(8.4)^(4x-10)#
Use the fact that:
#log(a)^x=xlog(a)#
So we get:
#xln(6.5)=(4x-10)ln(8.4)#
Rearrange:
#xln(6.5)-4xln(8.4)=-10ln(8.4)#
#x[ln(6.5)-4ln(8.4)]=-10ln(8.4)#
#x=(-10ln(8.4))/(ln(6.5)-4ln(8.4))=3.2#

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