Question

Ayudaaa
Doy lo mejor a la mejor respuesta ​

Answer 1

Respuesta:

Explicación paso a paso:

Si tienes calculado te saldrael log ok espero haberte ayudado

Answer 2

Porfa dame mejor respuestaa:

The logarithm properties are

1) Product Rule

The logarithm of a product is the sum of the logarithms of the factors.

loga xy = loga x + loga y

2) Quotient Rule

The logarithm of a quotient is the logarithm of the numerator minus the logarithm of the denominator

loga  = loga x - loga y

3) Power Rule

loga xn = nloga x

4) Change of Base Rule

where x and y are positive, and a > 0, a ≠ 1

Proof for the Product Rule

loga xy = loga x + loga y

Proof:

Step 1:

Let m = loga x and n = loga y

Step 2: Write in exponent form

x = am and y = an

Step 3: Multiply x and y

x • y = am • an = am+n

Step 4: Take log a of both sides and evaluate

log a xy = log a am+n

log a xy = (m + n) log a a

log a xy = m + n

log a xy = loga x + loga y

Proof for the Quotient Rule

loga  = loga x - loga y

Proof:

Step 1:

Let m = loga x and n = loga y

Step 2: Write in exponent form

x = am and y = an

Step 3: Divide x by y

x ÷ y = am ÷ an = am - n

Step 4: Take log a of both sides and evaluate

log a (x ÷ y) = log a am - n

log a (x ÷ y) = (m - n) log a a

log a (x ÷ y) = m - n

log a (x ÷ y) = loga x - loga y

Proof for the Power Rule

loga xn = nloga x

Proof:

Step 1:

Let m = loga x

Step 2: Write in exponent form

x = am

Step 3: Raise both sides to the power of n

xn = ( am )n

Step 4: Convert back to a logarithmic equation

log a xn = mn

Step 5: Substitute for m = loga x

log a xn = n loga x

Proof for the Change of Base Rule

 

Proof:

Step 1:

Let x = loga b

Step 2: Write in exponent form

ax = b

Step 3: Take log c of both sides and evaluate

log c ax = log c b

xlog c a = log c b