Question

9^x-2 =64(4^x)

Answer 1

is the question

\[9^{(x - 2)} = 64(4^x)\]

you can take to log of both sides... it doesn't matter if its base 10 or base e

Answer 2

Yes, solve the exponential equation. Round your solution to the nearest hundreth

Answer 3

i think you need a step first

Answer 4

since \(64=4^3\) the right hand side can be written as \(4^3\times 4^x=4^{x+3}\)
so now it is your job to solve
\[9^{x-2}=4^{x+3}\]

Answer 5

now we can work with the log
take the log of both sides, get
\[(x-2)\ln(9)=(x+3)\ln(4)\] and it is algebra from here on in

Answer 6

is it clear how to do the algebra?

Answer 7

Do I solve for ln or x?

Answer 8

you are looking for \(x\)

Answer 9

\(\ln(9)\) means the natural log of 9, it is a number

Answer 10

like saying \((x-2)f(9)=(x+3)f(4)\)
you cannot solve for \(f\) it is the name of the function

Answer 11

okay, so I need to isolate x

Answer 12

yes, that was the goal, to solve for \(x\)
distribute first

Answer 13

\[(x-2)\ln(9)=(x+3)\ln(4)\]
\[\ln(9)x-2\ln(9)=\ln(4)x+3\ln(4)\] is step one

Answer 14

do i then move ln to one side?

Answer 15

i sense that you are a bit confused
you are trying to find \(x\)
\(\ln\) is a function and \(\ln(9)\) is the function evaluated at 9, i.e. it is a number
you want to solve for \(x\). put all terms with \(x\) on one side of the equation, everything else on the other

Answer 16

suppose you want to solve \(2^x=12\) then you would say \(x\ln(2)=\ln(12)\) i.e. \(x=\frac{\ln(12)}{\ln(2)}\)
it is \(x\) you are looking for, \(\ln(2)\) is a number, namely the natural log of 2

Answer 17

Yes I am. I am taking this class online so I don't have much instruction. Thank you so much for the help so far!

Answer 18

ok is it clear that \(\ln(9)\) is a number?

Answer 19

it is about(2.197\)
http://www.wolframalpha.com/input/?i=ln%289%29

Answer 20

lets work this all out from this line
\[(x-2)\ln(9)=(x+3)\ln(4)\]
using the distributive property to remove the parentheses, you get
\[\ln(9)x-2\ln(9)=\ln(4)x+3\ln(4)\]
now we need all terms with \(x\) on one side, you can write
\[\ln(9)x-\ln(4)x=3\ln(4)+2\ln(9)\]

Answer 21

then factor out the \(x\) on the left get
\[\left(\ln(9)-\ln(4)\right)x=3\ln(4)+2\ln(9)\]

Answer 22

and finally divide to solve for \(x\) and get
\[x=\frac{3\ln(4)+2\ln(9)}{\ln(9)-\ln(4)}\]

Answer 23

everything on the right is a number
if you want a decimal, use a calculator, or use this
http://www.wolframalpha.com/input/?i= \frac{3\ln%284%29%2B2\ln%289%29}{\ln%289%29-\ln%284%29}

Answer 24

damn let me try again
http://www.wolframalpha.com/input/?i=%283ln%284%29%2B2ln%289%29%29%2F%28ln%289%29-ln%284%29%29

Answer 25

so x = 10.55 right

Answer 26

if rounding to the hundreth

Answer 27

yes