Final answer:
To solve the equation 82^x = 26 for x, we use logarithms to isolate x, resulting in x = ln(26) / ln(82).
Step-by-step explanation:
The question asks to solve for x in the equation 82x = 26. To find the value of x, we'll apply logarithms to both sides of the equation because logarithms allow us to bring down the exponent making it easier to solve for x. Here are the steps:
- Take the natural logarithm (ln) of both sides: ln(82x) = ln(26).
- Apply the power rule of logarithms, which states that ln(ab) = b*ln(a), giving us x*ln(82) = ln(26).
- To solve for x, divide both sides of the equation by ln(82), resulting in x = ln(26) / ln(82).
Thus, the value of x is the quotient of ln(26) divided by ln(82).