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Express the given expression without logs, in simplest form. Assume all variables represent positive values. (e^(ln(10 z)+ln(6y^(3)))) Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(eln⁡(10z)+ln⁡(6y3)) \left(e^{\ln (10 z)+\ln \left(6 y^{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⁡(10z)+ln⁡(6y3)) \left(e^{\ln (10 z)+\ln \left(6 y^{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⁡(10z)+ln⁡(6y3)e^{\ln(10z) + \ln(6y^3)} can be rewritten using this property.eln⁡(10z⋅6y3)e^{\ln(10z \cdot 6y^3)}
  2. Rewrite Using Property: Simplify the expression inside the logarithm.\newline10z×6y3=60zy310z \times 6y^3 = 60zy^3\newlineSo, eln⁡(10z)+ln⁡(6y3)e^{\ln(10z) + \ln(6y^3)} becomes eln⁡(60zy3)e^{\ln(60zy^3)}.
  3. Simplify Inside Logarithm: Use the property of exponents and logarithms that eln⁡(x)=xe^{\ln(x)} = x. eln⁡(60zy3)e^{\ln(60zy^3)} simplifies to 60zy360zy^3.

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