Question

What is the true solution to ln 20+ln 5= 2 ln x

Answer 1

Ln20+ln5=2lnx
ln(20x5)=lnx^2
ln100=1nx^2
100=x^2
square root
x=10

Answer 2

Answer:

The true solution to the  $\ln 20 + \ln 5 = 2 \ln x$ is, 10

Step-by-step explanation:

Given the equation: $\ln 20 + \ln 5 = 2 \ln x$

Using logarithmic rules:

• $\ln(mn) = \ln m+ \ln n$

• $\ln a^b = b \ln a$

• $ln a = \ln b$ ⇒$a = b$

Now, using these properties solve for x;

$\ln (20 \cdot 5) = 2\ln x$

$\ln (100) = \ln x^2$

$\ln 10^2 = \ln x^2$

On comparing both sides we have;

$x^2 = 10^2$

or

$x = \sqrt{10^2}$

x = 10

Therefore, the true solution to the given equation is, x= 10