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Write [tex]\( y = 10^x \)[/tex] as a logarithmic function.

A. [tex]\( \log_{10} y = x \)[/tex]
B. [tex]\( \log_x y = 10 \)[/tex]
C. [tex]\( \log_y x = 10 \)[/tex]
D. [tex]\( \log_x 10 = y \)[/tex]



Answer :

GinnyAnswer
To rewrite the exponential equation [tex]\( y = 10^x \)[/tex] as a logarithmic function, you can follow these steps:

1. Start with the given exponential equation:
[tex]\[ y = 10^x \][/tex]

2. Take the logarithm base 10 of both sides of the equation to rewrite it in logarithmic form:
[tex]\[ \log_{10}(y) = \log_{10}(10^x) \][/tex]

3. Use the logarithmic property that [tex]\(\log_b(a^c) = c \cdot \log_b(a)\)[/tex]. Applying this property:
[tex]\[ \log_{10}(10^x) = x \cdot \log_{10}(10) \][/tex]

4. Since [tex]\(\log_{10}(10)\)[/tex] equals 1 (because 10 raised to the power of 1 is 10):
[tex]\[ x \cdot \log_{10}(10) = x \cdot 1 = x \][/tex]

5. Therefore, the equation simplifies to:
[tex]\[ \log_{10}(y) = x \][/tex]

So, the correct way to write [tex]\( y = 10^x \)[/tex] as a logarithmic function is:
[tex]\[ \log_{10}(y) = x \][/tex]

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