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).