# Math

posted by .

My question says:
Find the exact alue of x for which (4^x)*(5^[4x+3])=(10^[2x+3])

I can't seem to come to a solution.
We're reviewing last year's lessons, so change of base and logarithmic expressions are what we're going over right now.

Here's what I've done so far:

(4^x)*(5^[4x+3])=(10^[2x+3])
log both sides
log[(4^x)*(5^[4x+3])]=log[(10^[2x+3])]
(xlog4)+([4x+3]log5)=([2x+3]log10)
since log10=1
(xlog4)+([4x+3]log5)=(2x+3)

Have I started correctly? Where do I go from here? Please be detailed, I want to understand this.

• Math -

Proceed and solve for x in terms of ln.
I get x=ln(8)/ln(25).

• Math -

How do I proceed? I really have no clue where to go from where I've stopped! Usually I can simply factor out an x from the LS, but here I can't do that. Could you please show me your solution with every step? It would be so helpful.

Thank you in advance :)

• Math -

It is a linear equation with numerical coefficients (log4, etc.).

Expand
(xlog4)+([4x+3]log5)=(2x+3)
to give
xlog4 + 4xlog5 - 2x = 3 -3log5
Factor out x on the LHS and solve for x.
All the log4, log5 are numerical values that you can simplify eventually.

• Math -

Sorry to keep bugging, but I followed what you told me and got to:

x=(3-[log125])/([log2500]-2)

How can I get to the answer from that? I don't know how to deal with the 3 and the -2 that are still lying around.

• Math -

Alright, what I did now was:

since log10=1, log100=2, and log1000=3

So I plugged that in to what I had

x=(log1000-log125)/(log2500-log100)
x=(log[1000/125])/(log[2500/100])
x=(log8)/(log25)

Is that what I was supposed to do?

## Similar Questions

1. ### algebra homework

please check my answers. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. ln sqrt x+6 = 9 i got {e^9-6} log (x + 4) = log (5x - 5) …
2. ### math 116

I am taking math 116 , I am to find the solution to the problem 9x-3y=-68 and -2x+y=18 and to give an ordered pair. Now, that you have it where you take 9x from both sides, or is it 3y?
3. ### pre calculus

solve the equation. give an exact solution, and also an approximate solution to four decimal places. 2^(9x-7)=7 My first step was to change it to log(base 2) 7 = 9x-7 i got 1.0897 Did i do something wrong or did i miss one question?
4. ### English

Can you help me determine if I chose the correct/incorrect sentences appropriately. It’s really urgent. 1)Jenny, 13, says “My favourite subject is English. We all have to learn English in my country because it is very difficult …
5. ### pre-calculus

solve the logarithmic equation. be sure to reject any value of x that is not in the domain of the orginal logarithmic expression. In square root of x+2=2 (If I try to make the square root sign it will not come out right so I wrote …
6. ### pre-calculus

solve the following logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give the exact answer. then, use the calculator to obtain a decimal appromiation, correct …
7. ### calculus

solve the logarithmic equation. be sure to reject any value of x that is not in the domain of the orginal logarithmic expression. In square root x+7=2 what is the exact solution?
8. ### adv functions

Hi! I need help with determining the value of each of the following logarithmic expressions. Do not change the bases- thx a) log[base8]4 b)log[base(1/3)]27
9. ### Math Logarithmic Question

Solve for all possible values of x within the domain of the following logarithmic expressions. a)logx+log2=log7−log3
10. ### Algebra

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. ln ã(x+4)=1 What is the exact solution?

More Similar Questions