Exponential and Logarithmic Functions

The general form of an exponential function can be expressed as y=a*b^x, in which 'a' represents a constant, 'b' identifies the base, and 'x' assumes the role of the exponent. Conversely, logarithmic functions, serving as the inverse of exponential functions, are represented by the equation y=log_b(x), where 'b' denotes the base. These particular functions play a pivotal role in various fields of mathematics and applied sciences.

Simplifying Logarithmic Expressions

Solve for \( x \) in the equation \( \log_{10}(2\cos x) = 1 \).

Expanding Logarithmic Expressions

Solve the equation \(2^{\cos x} = 8\) for \(x\), given that \(0 \leq x \leq 2\pi\).

Exponential Expressions

Find the value of the expression: \( e^{2\cos^{-1}(\frac{1}{2})} \)