Question
Solve logarithmic 5^(x+7)=3
Answers
Answered by
oobleck
pretty good, until the final answer:
(ln(3) / ln(5)) - 7 = -6.317
(ln(3) / ln(5)) - 7 = -6.317
Answered by
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
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
Answered by
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.
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.
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