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What is x if #lnx + ln5x^2 = 10#?

Answer 1

Avery Alexander

First, you should use the logarithm rule #log_a (x) + log_a (y) = log_a ( x * y)#

Here, it gives you: #" ln x + ln 5 x^2 = 10# #<=> " ln( x * 5 x^2) = 10# #<=> " ln(5 x^3) = 10#

Now, you can exponentiate both sides to get rid of the #ln#:

#<=> " e^(ln(5x^3)) = e^10#

... remember that #e# and #ln# are inverse functions...

#<=> " 5x^3 = e^10# #<=> " x^3 = (e^10) / 5# #<=> " x = root(3)((e^10) / 5)#

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Answer 2

Savannah Anderson

To find the value of ( x ), we can use the properties of logarithms to simplify the equation:

[ \ln{x} + \ln{5x^2} = 10 ]

[ \ln{(5x^3)} = 10 ]

[ 5x^3 = e^{10} ]

[ x^3 = \frac{e^{10}}{5} ]

[ x = \sqrt[3]{\frac{e^{10}}{5}} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.