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Exercise

$\ln y+2\ln x=\ln5$

Step-by-step Solution

1

Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $2$

$\ln\left(y\right)+\ln\left(x^2\right)=\ln\left(5\right)$
2

Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$

$\ln\left(yx^2\right)=\ln\left(5\right)$
3

For two logarithms of the same base to be equal, their arguments must be equal. In other words, if $\ln(a)=\ln(b)$ then $a$ must equal $b$

$yx^2=5$
4

Divide both sides of the equation by $x^2$

$y=\frac{5}{x^2}$

Final answer to the exercise

$y=\frac{5}{x^2}$

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Similar Questions Solved

$\log_x\left(64\right)=3$

$log\left(x+1\right)=log\left(x-1\right)+3$

$\log\left(x-1\right)+\log\left(x+1\right)=2\log\left(x+2\right)$

$\log_x\left(\frac{1}{8}\right)=-3$

$\log_x\left(100\right)-\log_x\left(25\right)=2$

$\log_2\left(x\right)-\log_2\left(10\right)=\log_2\left(9.3\right)$

$\log\left(\left(y+2\right)\right)=1+\log\left(\left(2y-6\right)\right)$

Main Topic: Properties of Logarithms

They are properties that can help us simplify expressions with logarithms.

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