Solve the given equation for x. 6^(4x−6)=43?

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Answer 1 · 2018-02-28T19:50:42

#x=ln(43)/ln(1296)+3/2#

Apply the natural logarithm to both sides:

#ln(6^(4x-6))=ln(43)#

#(4x-6)(ln(6))=ln(43)# (Because #ln(a^b)=bln(a)#)

Solve for #x:#

#(cancelln(6)(4x-6))/cancelln(6)=ln(43)/ln(6)#

#4xcancel(-6+6)=ln(43)/ln(6)+6#

#(cancel4x)/cancel4=(ln(43)/ln(6)+6)/4#

#x=ln(43)/(4ln(6))+6/4#

#x=ln(43)/ln(6^4)+3/2# (Because #bln(a)=ln(a^b)#

#x=ln(43)/ln(1296)+3/2#