Home > PC3 > Chapter 6 > Lesson 6.2.4 > Problem6-130

6-130.

Solve each of the following equations.

1. $50x^{2/3}=100$

Divide both side by $50$ first.
Then undo the exponent by raising both sides to the $3/2$ power

1. $\log_3(x+1)+\log_3(x)=\log_3(12)$

Combine the terms on the left side into one logarithm.

$\log_3\left(\left(x+1\right)\left(x\right)\right)=\log_3\left(12\right)$

1. $50(\frac{2}{3})^x=100$

Divide by $50$ first.
Then take the log of both sides, bringing the $x$ down in front.
Solve for $x$.

1. $\log_3(x+1)-\log_3(x)=\log_3(12)$

This problem is similar to part (b), except the subtraction indicates that you need to divide the arguments when creating the single logarithm instead of multiplying them.