How do you evaluate #5e^(3x+7)=21#?

1 Answer
mason m
Mar 6, 2016

#x=(ln(21/5)-7)/3approx-1.8550#

Explanation:

Divide both sides by #5#.

#e^(3x+7)=21/5#

To undo the exponential function with a base of #e#, take the logarithm of both sides with base #e#. Note that #log_e(x)# is the natural logarithm, denoted #ln(x)#.

#ln(e^(3x+7))=ln(21/5)#

#3x+7=ln(21/5)#

Subtract #7# from both sides.

#3x=ln(21/5)-7#

Divide both sides by #3#.

#x=(ln(21/5)-7)/3approx-1.8550#

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