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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$
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$x^2\cdot 2^x\left(\ln\left(2\right)+\ln\left(x\right)\right)$
Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the expression x^22^xln(2x). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Multiplying polynomials x^2 and \ln\left(2\right)+\ln\left(x\right). Multiply the single term 2^x by each term of the polynomial \left(\ln\left(2\right)x^2+x^2\ln\left(x\right)\right).