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Rewrite this exponential equation as a logarithmic equation.

[tex]\[ 4e^x = 16 \][/tex]

Sagot :

GinnyAnswer
To rewrite the given exponential equation [tex]\( 4 e^x = 16 \)[/tex] as a logarithmic equation, follow these steps:

1. Isolate the exponential term:
[tex]\[ e^x = \frac{16}{4} \][/tex]
Simplify the right side:
[tex]\[ e^x = 4 \][/tex]

2. Take the natural logarithm (ln) of both sides:
[tex]\[ \ln(e^x) = \ln(4) \][/tex]

3. Apply the logarithmic identity [tex]\(\ln(e^x) = x \cdot \ln(e)\)[/tex]:
[tex]\[ x \cdot \ln(e) = \ln(4) \][/tex]

4. Since [tex]\(\ln(e)\)[/tex] is 1, the equation simplifies to:
[tex]\[ x = \ln(4) \][/tex]

Therefore, the logarithmic equation is:
[tex]\[ x = \ln(4) \][/tex]
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