How do you solve #7.74^(x + 3) = 10.2#?

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Answer 1 · 2015-11-22T01:32:21

I found: #x-1.8651#

You can first take the natural log of both sides:

#ln(7.74)^(x+3)=ln(10.2)#

Then you can use the property of logs that tells us that:

#logx^b=blogx#

and write:

#(x+3)ln(7.74)=ln(10.2)#
rearrange:

#x+3=(ln(10.2))/ln(7.74)#
#x=(ln(10.2))/ln(7.74)-3#
#x=1.1348-3=-1.8651#