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Express the given expression without logs, in simplest form. Assume all variables represent positive values. (e^(ln(4w)+ln(10x^(3)))) Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(eln⁡(4w)+ln⁡(10x3)) \left(e^{\ln (4 w)+\ln \left(10 x^{3}\right)}\right) \newlineAnswer:

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Full solution

Q. Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(eln⁡(4w)+ln⁡(10x3)) \left(e^{\ln (4 w)+\ln \left(10 x^{3}\right)}\right) \newlineAnswer:
  1. Apply Logarithm Property: Use the property of logarithms that ln⁡(a)+ln⁡(b)=ln⁡(ab)\ln(a) + \ln(b) = \ln(ab).eln⁡(4w)+ln⁡(10x3)e^{\ln(4w) + \ln(10x^{3})} can be rewritten using this property as eln⁡(4w⋅10x3)e^{\ln(4w \cdot 10x^{3})}.
  2. Simplify Inside Logarithm: Simplify the expression inside the logarithm. \newline4w×10x34w \times 10x^{3} simplifies to 40wx340wx^{3}.\newlineSo, eln⁡(4w)+ln⁡(10x3)e^{\ln(4w) + \ln(10x^{3})} becomes eln⁡(40wx3)e^{\ln(40wx^{3})}.
  3. Use Exponent Property: Use the property of logarithms and exponents that eln⁡(a)=ae^{\ln(a)} = a. Since the base of the natural logarithm (ln⁡\ln) is ee, we can simplify eln⁡(40wx3)e^{\ln(40wx^{3})} to just 40wx340wx^{3}.
  4. Check for Simplifications: Check for any possible simplifications or reductions. The expression 40wx340wx^{3} is already in its simplest form, assuming ww and xx are variables representing positive values.

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