The Exact Solution to an Exponential Equation Such As $2 ^ { x } = 3$

question 396

Multiple Choice

The exact solution to an exponential equation such as $2 ^ { x } = 3$ can be expressed in three forms: $\log _ { 2 } 3 , \frac { \log 3 } { \log 2 }$ , or $\frac { \ln 3 } { \ln 2 }$ . Give the exact solution to the following exponential equation in three forms.
$$3 ^ { x } = 15$$

• A) \(\log _ { 3 } 15 ; \frac { \log 3 } { \log 15 } ; \frac { \ln 3 } { \ln 15 }\)
• B) \(\log _ { 15 } 3 ; \frac { \log 3 } { \log 15 } ; \frac { \ln 3 } { \ln 15 }\)
• C) \(\log 153 ; \frac { \log 15 } { \log 3 } ; \frac { \ln 15 } { \ln 3 }\)
• D) \(\log _ { 3 } 15 ; \frac { \log 15 } { \log 3 } ; \frac { \ln 15 } { \ln 3 }\)

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Definitions:

Innocent

Innocent refers to not being guilty of a crime or offense, or lacking knowledge of wrongdoing.

Void

Void refers to a legal declaration that a contract or transaction is null, having no effect or force in law, typically due to failing to meet certain legal requirements.

Mistake

An error or misunderstanding in the terms or conditions of a contract that can lead to its revocation or modification if all parties agree or if a court intervenes.

Mortgage

A legal agreement where property is used as security for a loan, with the condition that the conveyance of title becomes void upon repayment of the loan.