mth

· Check out this example for how to solve exponent variables using natural logarithms.

· Solve 5x = 212.

Since 212 is not a power of 5, then I will have to use logs to solve this equation. I could take base-5 log of each side, solve, and then apply the change-of-base formula, but I think I'd rather just use the natural log in the first place:

5x = 212

ln(5x) = ln(212)

xln(5) = ln(212) 

x = ln(212)/ln(5)

...or about 3.328, rounded to three decimal places.

You can also use the "log" function instead of the natural log "ln" to solve for exponents.

· Using what you learned and the example problem I posted in this discussion starter solve the following equation for x using logarithms.

 

3x = 81

 

Show you work.