Write 6^(5)=7776 in logar (A) log_(6)5=7776 (B) log_(6)7776=5 (C) log_(5)6=7776 (D) log_(5)7776=6

Understand Relationship: Understand the relationship between exponential and logarithmic forms. The exponential form b^y = x can be rewritten in logarithmic form as log_b(x) = y, where b is the base, y is the exponent, and x is the result.Identify Values: Identify the base (b), exponent (y), and result (x) in the given exponential equation. In the equation 6^(5)=7776, the base (b) is 6, the exponent (y) is 5, and the result (x) is 7776.Convert to Logarithmic Form: Convert the exponential equation to logarithmic form using the relationship from Step 1. Using the identified values, the logarithmic form of the equation is log_6(7776) = 5.Match with Options: Match the converted logarithmic equation with the given options. The correct logarithmic form is log_6(7776) = 5, which matches option (B).

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Write $6^{5}=7776$ in logarithmic form $\newline$ (A) $\log_{6}5=7776$ $\newline$ (B) $\log_{6}7776=5$ $\newline$ (C) $\log_{5}6=7776$ $\newline$ (D) $\log_{5}7776=6$

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Math Problems

Algebra 2

Convert between exponential and logarithmic form: all bases

Full solution

Q. Write

6^{5}=7776

in logarithmic form

\newline

(A)

\log_{6}5=7776

\newline

(B)

\log_{6}7776=5

\newline

(C)

\log_{5}6=7776

\newline

(D)

\log_{5}7776=6

Understand Relationship: Understand the relationship between exponential and logarithmic forms. The exponential form $b^y = x$ can be rewritten in logarithmic form as $\log_b(x) = y$ , where $b$ is the base, $y$ is the exponent, and $x$ is the result.
Identify Values: Identify the base $b$ , exponent $y$ , and result $x$ in the given exponential equation. $\newline$ In the equation $6^{5}=7776$ , the base $b$ is $6$ , the exponent $y$ is $5$ , and the result $x$ is $7776$ .
Convert to Logarithmic Form: Convert the exponential equation to logarithmic form using the relationship from Step $1$ . $\newline$ Using the identified values, the logarithmic form of the equation is $\log_6(7776) = 5$ .
Match with Options: Match the converted logarithmic equation with the given options. $\newline$ The correct logarithmic form is $\log_6(7776) = 5$ , which matches option $(B)$ .