solve 6 = 15^1-x by using logarithms. Round your asnwer to the nearest thousandth. PLease help?
take the log of each side..
log6=(1-x)log15
log6/log15=1-x
x= 1-log6/log15
check that
thank you
x2/y2
To solve the equation 6 = 15^(1-x) using logarithms, we can take the logarithm of both sides of the equation. Specifically, we can use the natural logarithm (ln) or the common logarithm (log) to simplify the equation.
Let's work through the steps:
Step 1: Take the logarithm of both sides of the equation.
ln(6) = ln(15^(1-x))
Step 2: Apply the power rule of logarithms.
ln(6) = (1-x) * ln(15)
Step 3: Divide both sides by ln(15) to isolate (1-x).
(1-x) = ln(6) / ln(15)
Step 4: Simplify the right side of the equation.
(1-x) = ln(6 / 15)
Step 5: Use a calculator to evaluate ln(6/15) and round your answer to the nearest thousandth.
(1-x) ≈ -0.607
Step 6: Solve for x by subtracting 1 from both sides
-x ≈ -0.607 - 1
x ≈ 1.607
Therefore, the approximate solution to the equation 6 = 15^(1-x), rounded to the nearest thousandth, is x ≈ 1.607.