Question

Log_5(5-3x)=2log_5 2СРОЧНО

Answer 1

2log5 2=log5  $2^{2}$ по формуле
log5 (5-3x)=log5 4
5-3x=4
-3x=4-5
-3x=-1
x=1/3

Answer 2

To solve the logarithmic equation $\log_5(5-3x) = 2\log_5 2$, we can use the properties of logarithms to simplify and solve for $x$:

1. Apply the logarithmic property $\log_a(b^n) = n\log_a(b)$:

   $\log_5(5-3x) = \log_5(2^2)$

2. Simplify the right side:

   $\log_5(5-3x) = \log_5(4)$

3. Since both sides have the same base ($5$) and the same logarithm value, we can drop the logarithm notation:

   $5 - 3x = 4$

4. Now solve for $x$:

   $5 - 4 = 3x$

   $1 = 3x$

   $x = \frac{1}{3}$

So, the solution to the equation is $x = \frac{1}{3}$.