15^4x=4^x-4
Solve for x. Write the exact answer using the base-10 logarithms.

Question

15^4x=4^x-4
Solve for x. Write the exact answer using the base-10 logarithms.

hy123 · Answer

$$15^{4x}=4^{x-4}$$

ganeshie8 · Answer

$$\huge 15^{4x} = 4^{x-4}$$

its like this ?

hy123 · Answer

Yeah.

ganeshie8 · Answer

take log on both sides

hy123 · Answer

I did that.

hy123 · Answer

Wouldn't you just make it so they both change to 60 and then multiply the exponent by the number you used to get to 60?

ganeshie8 · Answer

$$\huge log\ m^n = nlog\ m$$

ganeshie8 · Answer

i see.. you trying to solve for x without using log ?

hy123 · Answer

Well they want the exact answer using the base-10 log

ganeshie8 · Answer

question is asking to leave the answer in log terms.. 
so we can simply separate the x

hy123 · Answer

So I'm going to guess they want it in log terms.

ganeshie8 · Answer

yeah... u r correct

hy123 · Answer

Is it that simply?
4xlog15=x-4log4?

ganeshie8 · Answer

yup... u forgot the parantheses.. 

4xlog15=(x-4)log4

hy123 · Answer

So that's all they are asking for when they say solve for x?

hy123 · Answer

Because they want me to slve for x while writing the answer in log terms.

ganeshie8 · Answer

yeah... but we still need to separate the x completely

hy123 · Answer

Ahh okay lol.

hy123 · Answer

Mind showing me the steps? I'm not really sure how to get there.

ganeshie8 · Answer

4xlog15=(x-4)log4

ganeshie8 · Answer

4xlog15 = xlog4 - 4log4

ganeshie8 · Answer

subtract xlog4 so that all x terms come one side

hy123 · Answer

4xlog15-xlog4=-4log4

ganeshie8 · Answer

yep..
now factor x

hy123 · Answer

x(4log15-log4)=-4log4?

ganeshie8 · Answer

yh..

hy123 · Answer

So the answer is (-4log4)/(4log15-log4)?

ganeshie8 · Answer

yep.. thats it. 
 if u dont like minus sign on top, reverse the order of subtraction on base..

hy123 · Answer

Well i dont mind. Thanks very much.

ganeshie8 · Answer

welcome... good work :))