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Question

Re write the exponentian equatiin in equivalent logarithmic form

1) e² =7.389

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if possible write the expressions using sums and/or difference of logarithmic expressions that do not contain the logarithms of products, quotients, or powers

1) ln(x(7-x)³)

2) ln(xy²/z)

Answer 1

1) ln=log with a base of e, so 

 

ln7.389=2

The exponent goes on the other side of the equal sign and the answer to the exponential equation goes  after the ln or log.

Answer 2

Write e^2 = 7.389 in equivalent logarithmic form.

 

The base is e. The exponent is 2. The number is 7.389.

 

log_base(number) = exponent

 

log_e(7.389) = 2

 

By convention, log_e is written as ln and pronounced "lawn".

 

ln(7.389) = 2 is equivalent to e^2 = 7.389.

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if possible write the expressions using sums and/or difference of logarithmic expressions that do not contain the logarithms of products, quotients, or powers

 

1) ln(x(7-x)^3) = L

 

Apply Product Rule of Logarithms:

 

L = ln(x) + ln((7-x)^3)

 

Apply Power Rule of Logarithms:

 

L = ln(x) + 3*ln(7-x)

 

 

2) ln(xy^2/z) = L

 

Apply Quotient Rule of Logarithms:

 

L = ln(xy^2) – ln(z)

 

Apply Product Rule of Logarithms:

L = ln(x) + ln(y^2) – ln(z)

 

Apply Power Rule of Logarithms:

 

L = ln(x) + 2*ln(y) – ln(z)