Solve for X if #3^(x+5)=27^(-2x+1)#?

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Answer 1 · 2018-05-30T08:36:44

#x=-2/7#

#color(blue)(3^(x+5)=27^(-2x+1)#

To solve questions like this, we need to make the bases same.

#rarr3^(x+5)=(3*3*3)^(-2x+1)#

#rarr3^(x+5)=(3^3)^(-2x+1)#

Use, #color(brown)((a^b)^c=(a^(bc))#

#rarr3^(x+5)=3^(-6x+3)#

Since, the bases are same, if #color(brown)(a^b=a^c# then #color(brown)(b=c#

So,

#rarrx+5=-6x+3#

#rarrx+6x=3-5#

#rarr7x=-2#

#color(green)(rArrx=-2/7#

Hope that helps!...#phi#