need help im confused

Question

Solve each equation for t.  Show the work that leads for your solution. Your answers may be exact or correct to at least 3 places after the decimal point. 

 5 * 10^t  = 250

t = 

 

Answer 1

Hi Logan V.,

The way you solve the equation above is to successively "peel away" the things that are "concealing" it.

In the language of math, you apply inverse operations to do this. Consider t first of all. What is "concealing" it? Let's make a list: It's propped up as an exponent of 10. And then, beyond that, that whole thing is multiplied by 5. It doesn't matter what order things are written in the equation, you go by the PEMDAS rules first. And E=exponents are before M=multiplication. But that's for when you evaluate (calculate) the expression; for the "unpeeling" you do the opposite order.

Why? Imagine the calculation is like a zipper: per PEMDAS you start zipping the "t" from the bottom (the exponentiation), and then you do the multiplication (near the top of the zipper track). So to unzip, you have to go 'top to bottom' in the unzipping. So, you unpeel in the reverse order to how you zipped up.

So:

Divide both sides of the equality by 5: -->

10^t = 50

Next, undo the exponentiation operation: that's taking the log:

log(10^t) = t*log 10 = log(50) ≅ 1.69897 where ≅ means "approximately equal to".

t*1 = 1.69897

t = 1.699 to three decimal places beyond the decimal point.

-- Cheers, --Mr. d.

Answer 2

Hi Logan V.,

The way you solve the equation above is to successively "peel away" the things that are "concealing" it.

In the language of math, you apply inverse operations to do this. Consider t first of all. What is "concealing" it? Let's make a list: It's propped up as an exponent of 10. And then, beyond that, that whole thing is multiplied by 5. It doesn't matter what order things are written in the equation, you go by the PEMDAS rules first. And E=exponents are before M=multiplication. But that's for when you evaluate (calculate) the expression; for the "unpeeling" you do the opposite order.

Why? Imagine the calculation is like a zipper: per PEMDAS you start zipping the "t" from the bottom (the exponentiation), and then you do the multiplication (near the top of the zipper track). So to unzip, you have to go 'top to bottom' in the unzipping. So, you unpeel in the reverse order to how you zipped up.

So:

Divide both sides of the equality by 5: -->

10^t = 50

Next, undo the exponentiation operation: that's taking the log:

log(10^t) = t*log 10 = log(50) ≅ 1.69897 where ≅ means "approximately equal to".

t*1 = 1.69897

t = 1.699 to three decimal places beyond the decimal point.

-- Cheers, --Mr. d.

Answer 3

Divide both sides by 5 to isolate the exponent term.

10^t  = 25

Rewrite as a log

log₁₀25 = t

Using the calculator

t=1.398