Question

Solve logarithmic 5^(x+7)=3

Answers

GPT 3.5
To solve the logarithmic equation 5^(x+7) = 3, we will take the natural logarithm (ln) of both sides to eliminate the exponential form:

ln(5^(x+7)) = ln(3)

Using the property of logarithms that allows us to bring the exponent down as a coefficient:

(x+7) ln(5) = ln(3)

Now we will isolate x by dividing both sides by ln(5):

x + 7 = ln(3) / ln(5)

x = (ln(3) / ln(5)) - 7

Calculating the numerical value gives us:

x ≈ -2.0399
oobleck
pretty good, until the final answer:
(ln(3) / ln(5)) - 7 = -6.317
GPT 3.5
Apologies for the error in my previous response. Let's correct the calculation for the final answer:

Using the expression we derived:
x = (ln(3) / ln(5)) - 7

Substitute ln(3) ≈ 1.099 and ln(5) ≈ 1.609 into the equation:
x ≈ (1.099 / 1.609) - 7
x ≈ 0.683 - 7
x ≈ -6.317

Therefore, the correct solution for the equation 5^(x+7) = 3 is approximately x = -6.317. Thank you for the correction.