How do you solve this using logarithms?

Question

Use logarithms to find #x#

#3(x)^0.6223=1.266#

Sadie Alexander · Accepted Answer

#color(blue)(x=e^((ln(0.422))/0.6223)~~0.2499763052)#

#3x^(0.6223)=1.266#

Divide by 3:

#x^(0.6223)=0.422#

Taking natural logarithms of both sides:

#0.6223ln(x)=ln(0.422)#

Divide by #0.6223#:

#ln(x)=(ln(0.422))/0.6223#

Raising #bbe# to the power of each side:

#e^(ln(x))=e^((ln(0.422))/0.6223)#

#x=e^((ln(0.422))/0.6223)~~0.2499763052#

Sadie Alexander · Answer

undefined To solve the inequality $ -8 < x - 11 < -6 $ using logarithms, we can follow these steps:

1. Start with the original inequality: $ -8 < x - 11 < -6 $.

2. Add 11 to all parts of the inequality to isolate $x$:
   $$ -8 + 11 < x - 11 + 11 < -6 + 11 $$
   This simplifies to:
   $$ 3 < x < 5 $$

3. Now, let's express the inequality using logarithms. We'll take the logarithm of each part of the inequality, using the natural logarithm (ln) for simplicity:
   $$ \ln(3) < \ln(x) < \ln(5) $$

4. Finally, simplify the expression:
   $$ \ln(3) < \ln(x) < \ln(5) $$

So, the solution to the inequality using logarithms is $ \ln(3) < \ln(x) < \ln(5) $.

How do you solve this using logarithms?

Use logarithms to find #x# #3(x)^0.6223=1.266#

Use logarithms to find #x#

#3(x)^0.6223=1.266#