Use Mathematical Induction to Prove the Following Equality , Where $x _ { 1 } > 0 , x _ { 2 } > 0 , \ldots , x _ { n } > 0$

question 20

Essay

Use mathematical induction to prove the following equality. $\quad \ln \left( 3 ^ { n } x _ { 1 } x _ { 2 } \ldots x _ { n } \right) = \ln \left( 3 x _ { 1 } \right) + \ln \left( 3 x _ { 2 } \right) + \ldots + \ln \left( 3 x _ { n } \right)$ , where $x _ { 1 } > 0 , x _ { 2 } > 0 , \ldots , x _ { n } > 0$ $x _ { 1 } > 0 , x _ { 2 } > 0 , \ldots , x _ { n } > 0$

Analyze how external factors like technology, government policies, and individual financial decisions affect the financial market.

Apply discounting techniques to assess the present value of future cash flows and investments.

Evaluate the impact of investment decisions on firm profitability and individual financial well-being.

Interpret the implications of debt management strategies on personal finance.

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Definitions:

Incidental Damages

Compensation for additional unexpected expenses that arise directly from a breach of contract, beyond the direct loss or damage incurred.

Breach

The violation or breaking of a legal obligation or agreement, which can result in legal action against the party that fails to honor their part of the contract.

Lessor

The party or entity that leases or rents property to another party, known as the lessee, under a lease agreement.

Liquidated Damages Clause

A contractual provision specifying a predetermined amount of damages to be paid if one party breaches the contract.