Answer :
Final answer:
The logarithmic equation log5(x(x-24))=2 converts to the exponential form as 5² = x(x-24). The conversion of exponential equation eˣ+1=4 to a logarithmic form results in ln(4-1) = x.
Explanation:
To convert the logarithmic equation log5(x(x-24))=2 to an exponential equation, we change from logarithm form to exponent form. The base of the logarithm becomes the base of the power, the right-hand side of the equation becomes the exponent, and the expression inside the log becomes the result of the power. Therefore, the exponential form is 5² = x(x-24).
Similarly, to convert the exponential equation eˣ+1=4 to a logarithmic equation, we use the formula logb(a) = c equivalent to [tex]b^c[/tex] = a, where b is the base number, a is the number, and c is the exponent. In this case, it becomes ln(4-1) = x, where 'ln' stands for the natural logarithm that has the base of 'e'.
Learn more about Logarithmic and Exponential Conversions here:
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