4^(x + 2) = 200
ln(4^(x+2) = ln(200)
xln(4) + 2ln(4) = ln(200)
xln(4) = -2ln(4) + ln(200)
xln(4)/ln(4) = (-2ln(4) + ln(200))*1/ln(4)
x = (-2ln(4) + ln(200))* 1/ln(4)
x = -2ln(4) + ln(200)/ln(4)
= 1.04
What am I doing wrong?
4^(x + 2) = 200
ln(4^(x+2) = ln(200)
xln(4) + 2ln(4) = ln(200)
xln(4) = -2ln(4) + ln(200)
xln(4)/ln(4) = (-2ln(4) + ln(200))*1/ln(4)
x = (-2ln(4) + ln(200))* 1/ln(4)
x = -2ln(4) + ln(200)/ln(4)
= 1.04
What am I doing wrong?
If you are going to divide the RHS by ln(4), then the -2ln(4) term becomes just -2.
You removed the parenthesis but didn't cancel out that term.
Btw, the easier way to solve this is just
log_4 (200) = x + 2
Then use change of base formula to compute log_4 (200). You'll get the same answer either way, but save a few steps.
Hi!
$\displaystyle 4^{x+2}=200 $
$\displaystyle (x+2)\cdot ln(4)=ln(200) $
$\displaystyle x\cdot ln(4)=ln(200)-2\cdot ln(4) $
$\displaystyle \Rightarrow \; x = \frac{ln(200)-2\cdot ln(4)}{ln(4)} $
Note: This can be simplified etc, but I didnt bother there, hoping it is easier to follow.