FInd x, round to the nearest hundredth. 4^x-5=6

Answer 1

1.73 if you mean 4^x = 6 +5 = 11

then log4(11) = x

4 to what power = 11?

1<x<2 since 4^1=4 and 4^2 = 16. 11 is closer to 16 than to 4, so x is closer to 2 than to 1

but x-5 = 1.29 if you mean 4^(x-5) = 6, you might have implicit parentheses around x-5

then x = 6.29

either way, you need a scientific calculator, or at least a calculator with logs common or natural

x = log11/log4 or = ln11/ln4 = log4(x) = 1.73

or if you had implicit parentheses around x-5 then

x-5 = log6/log4 or ln6/ln4 = log4(x-5) = 1.29,

x=1.29+5 = 6.29

Answer 2

Hello Kush!

4^x = 11 is the equation we want to solve, right? (I isolated the variable term by adding 5 to both sides)

To solve this, we have to use the good old "natural log" function---specifically "log of power". This page is a nice little review.

ln(4^x) = ln(11) [did the natural log on both sides]

x ln(4) = ln(11) [the exponent goes in front]

x = ln(11)/ln(4) [isolate x]

Now you just need to pop ln(11) divided by ln(4) into a calculator!