Final answer:
In order to solve the exponential equations, we use logarithms to bring down the exponents and isolate the variable. For each equation, we show the step-by-step process to find the value of x.
Step-by-step explanation:
a.) To solve the equation 2^(x/3) = 26, we need to isolate x. We start by taking the logarithm (log base 2) of both sides to bring down the exponent. This gives us x/3 = log2(26). To isolate x, we multiply both sides by 3 to get x = 3 * log2(26). Using a calculator, we can approximate the numerical value of x.
b.) To solve the equation 9 = 4^(2x-1), we first rewrite 9 as 3^2. Now, we can rewrite the equation as 3^2 = (2^2)^(2x-1). Using the property of exponents, we simplify the equation to 3^2 = 2^(4x-2). Taking the logarithm (log base 2) of both sides, we get 2(4x-2) = log2(9). Solving for x, we find the numerical value.
c.) To solve the equation 20(0.5)^(x/4) = 8, we start by dividing both sides by 20 to isolate the exponential term. This gives us (0.5)^(x/4) = 8/20 = 0.4. Taking the logarithm (log base 0.5) of both sides to bring down the exponent, we get x/4 = log0.5(0.4). Multiplying both sides by 4, we find the value of x.
Learn more about Solving Exponential Equations