Question

1)ln(4x -1) = 3 2)e^lnx=x.(prove) 3)? = 3 х  -4  -6 х  -4   4)Log2(5x+7)=5

Answer 1

в чем смысл задания , понять не могу ?

Answer 2

Let's solve each of the equations one by one:

1. ln(4x - 1) = 3:

To solve this equation, we can start by exponentiating both sides with the base 'e' (natural logarithm):

e^(ln(4x - 1)) = e^3

Using the property that e^(ln(x)) = x, we have:

4x - 1 = e^3

Now, we can isolate the variable 'x' by adding 1 to both sides:

4x = e^3 + 1

Finally, divide both sides by 4 to solve for 'x':

x = (e^3 + 1) / 4

2. e^ln(x) = x (to be proven):

To prove this equation, we need to use the properties of logarithms and exponentials. Let's start by taking the natural logarithm of both sides:

ln(e^ln(x)) = ln(x)

Using the property that ln(e^x) = x, we have:

ln(x) = ln(x)

This shows that both sides are equal, so the equation e^ln(x) = x holds true.

3. ? = 3x - 4 - 6x - 4:

To solve this equation, we can combine like terms:

? = (3x - 6x) - (4 + 4)

Simplifying further:

? = -3x - 8

4. Log2(5x + 7) = 5:

To solve this equation, we can start by rewriting it in exponential form:

2^5 = 5x + 7

Simplifying the left side:

32 = 5x + 7

Next, subtract 7 from both sides:

32 - 7 = 5x

25 = 5x

Finally, divide both sides by 5 to solve for 'x':

x = 25 / 5

x = 5