solve 7^5x=23. round to the nearest ten-thousandth

also solve in (4x +5)=4 round to the nearest thousandth

7^5=16807/23=730.7391

4x+5=4
-5 -5
4x=9
4 4

x=2.25

233

To solve the equation 7^(5x) = 23, we need to isolate the variable "x".

Step 1: Take the logarithm of both sides of the equation. We can choose any base for the logarithm, but let's use the natural logarithm (base e) for this example.

ln(7^(5x)) = ln(23)

Step 2: Apply the exponent rule of logarithms, which states that log_b(x^y) = y * log_b(x).

5x * ln(7) = ln(23)

Step 3: Divide both sides of the equation by 5 * ln(7) to isolate "x".

x = ln(23) / (5 * ln(7))

Now, we can use a calculator to evaluate this expression and round it to the nearest ten-thousandth.

Using a calculator, you can find that x ≈ 0.2164 (rounded to four decimal places).

Moving on to the second equation, (4x + 5) = 4, we need to solve for "x".

Step 1: Subtract 5 from both sides of the equation.

4x = 4 - 5

Step 2: Simplify the right side of the equation.

4x = -1

Step 3: Divide both sides of the equation by 4 to isolate "x".

x = -1/4

Therefore, x = -0.25 (rounded to three decimal places).