How do you solve #ln (sqrt(x+9)) = 1#?

1 Answer
Johnson Z.
Mar 28, 2016

#x~~-1.61#

Explanation:

#1#. Use the natural logarithmic property, #ln_color(purple)b(color(purple)b^color(darkorange)x)=color(darkorange)x#, to rewrite the right side of the equation.

#ln(sqrt(x+9))=1#

#ln(sqrt(x+9))=ln(e^1)#

#2#. Since the equation now follows a "#ln=ln#" situation, where the bases are the same on both sides, rewrite the equation without the "ln" portion.

#sqrt(x+9)=e#

#3#. Solve for #x#.

#x+9=e^2#

#x=e^2-9#

#color(green)(|bar(ul(color(white)(a/a)x~~-1.61color(white)(a/a)|)))#

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