Those are the only ones I can't seem to resolve. Thank you!

resolve x:

1) 9*3^0,51x = 315

2) 10*3^15x+21 =363*2^9x+51

3) log(15x^2) - log(3x) = 4*log(3)

4) log[of base 3]*(15x + 4) = 3

To resolve the equations you provided, we can use algebraic techniques to isolate the variable x. Let's go through each equation step by step:

1) 9*3^(0.51x) = 315

To solve this equation, we want to get x by itself on one side. In this case, we can start by dividing both sides of the equation by 9:

3^(0.51x) = 35

Now, we can take the logarithm of both sides of the equation using any base. Let's choose the natural logarithm (log base e) because it's commonly used:

ln(3^(0.51x)) = ln(35)

Using the logarithmic property, we can bring the exponent down in front of the logarithm:

0.51x * ln(3) = ln(35)

Finally, to isolate x, divide both sides of the equation by 0.51 * ln(3):

x = ln(35) / (0.51 * ln(3))

2) 10*3^(15x+21) = 363*2^(9x+51)

Similarly to equation 1, let's divide both sides of the equation by 10:

3^(15x+21) = (363*2^(9x+51)) / 10

Now, take the logarithm of both sides with the base of your choice. Again, we will use the natural logarithm:

ln(3^(15x+21)) = ln((363*2^(9x+51)) / 10)

Using the logarithmic properties, we can bring the exponents down in front of the logarithm:

(15x+21)*ln(3) = ln((363*2^(9x+51)) / 10)

This equation doesn't simplify further, so we recommend using a numerical method or calculator to approximate the value of x.

3) log(15x^2) - log(3x) = 4*log(3)

Start by combining the logarithms on the left side of the equation using the quotient rule:

log(15x^2 / 3x) = 4*log(3)

Simplify within the logarithm:

log(5x) = 4*log(3)

Next, divide both sides of the equation by log(3):

log(5x) / log(3) = 4

Now, using the logarithmic property, you need to convert the logarithmic equation into an exponential equation:

3^(log(5x) / log(3)) = 3^4

Simplifying the right side:

5x = 81

Divide both sides by 5 to solve for x:

x = 81 / 5

4) log(base 3)(15x + 4) = 3

To resolve this equation, start by using the logarithmic property to convert it into exponential form:

3^3 = 15x + 4

Simplify the left side:

27 = 15x + 4

Subtract 4 from both sides:

23 = 15x

Finally, divide both sides by 15:

x = 23 / 15

These are the step-by-step solutions for the equations you provided. Make sure to double-check the answers and the steps, as there could be a possibility of errors during the calculation process.