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Which logarithmic equation is equivalent to the exponential equation below?

[tex]9^x=27[/tex]

A. [tex]9 = \log_{27} x[/tex]
B. [tex]x = \log_9 27[/tex]
C. [tex]27 = \log_9 x[/tex]
D. [tex]x = \log_{27} 9[/tex]

Sagot :

GinnyAnsweridn
To determine the logarithmic equation equivalent to the exponential equation \( 9^x = 27 \), we can follow the general properties of logarithms.

When dealing with an exponential equation of the form \( a^b = c \), it can be transformed into a logarithmic equation as \( b = \log_a(c) \).

Here, our equation is \( 9^x = 27 \).

We want to rewrite this in logarithmic form. According to the property, we should set:
[tex]\[ x = \log_9(27) \][/tex]

Therefore, the equivalent logarithmic equation is:
[tex]\[ x = \log_9(27) \][/tex]

So, the correct answer is:
B. [tex]\( x = \log_9 27 \)[/tex]
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