6. Exponential and Logarithmic Functions

Introduction to Logarithms

6. Exponential and Logarithmic Functions

Introduction to Logarithms

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Multiple Choice

Change the following exponential expression to its equivalent logarithmic form.
$3^{x}=7$

$\log_37=x$

$\log_73=x$

$\log_3x=7$

$\log7=3^{x}$

Verified step by step guidance

Identify the base of the exponential expression. In the expression $3^x = 7$, the base is 3.

Recognize that the exponential expression $3^x = 7$ can be rewritten in logarithmic form. The general form of converting an exponential expression $a^b = c$ to logarithmic form is $\log_a(c) = b$.

Apply the conversion rule to the given expression. Here, $a = 3$, $b = x$, and $c = 7$. Therefore, the logarithmic form is $\log_3(7) = x$.

Understand that the logarithmic form $\log_3(7) = x$ represents the power to which the base 3 must be raised to obtain the number 7.

Verify the conversion by checking that the base and the result match the original exponential expression. The base 3 raised to the power $x$ equals 7, confirming the logarithmic form $\log_3(7) = x$.