Question

Write in exponential form calculator

A) $e{ˡn(x)}$
B) $x{ˡog(x)}$
C) $10{ˡog₁₀(x)}$
D) $2{ˡog₂(ˣ)}

Answer 1

Expressions A, B, C, and D in exponential form simplify to x, utilizing the property that a base raised to the power of its own logarithm equals the number itself.

Step-by-step explanation:

To write expressions in exponential form, one must understand the relationship between exponentials and logarithms. Here are the given expressions written in exponential form:

• A) e^{ln(x)} simplifies to x because ln (natural log) and e (exponential function) are inverse functions.
• B) x^{log(x)} simplifies to x because the base and the logarithm have the same base, which cancels each other out.
• C) 10^{log_{10}(x)} simplifies to x as log_{10} is the common logarithm implying base 10, thereby cancelling each other out.
• D) 2^{log_{2}(x)} simplifies to x because the base and the logarithm are the same, which results in the exponent and the logarithm cancelling each other out.

Remember, the general rule states that a number b raised to the power of its own logarithm equals the number itself, symbolically represented as b^{log_{b}(x)} = x.