Check My Logs & Exponential Homework Answers

[zebra1707]

Homework Statement

Greetings - can someone please check my work, many thanks

Homework Equations

If x = 12.4 Find the value of ... correct to two sig fgures

8^(4x/3) / log(base 10) (5x-3/x^0)

The Attempt at a Solution

= 8^(16 8/15) / log(base 10) (5(12.4)-3 / 1)
= 4.8 x 10^14 (via calc 4.818429574)

Many thanks

 

[Mark44]

Homework Statement

Greetings - can someone please check my work, many thanks

Homework Equations

If x = 12.4 Find the value of ... correct to two sig fgures

8^(4x/3) / log(base 10) (5x-3/x^0)

This expression, (5x-3/x^0), is ambiguous. Is it (5x - 3)/1 or 5x - (3/1)? If it's the former, you're missing some needed parentheses.

The Attempt at a Solution

= 8^(16 8/15) / log(base 10) (5(12.4)-3 / 1)
= 4.8 x 10^14 (via calc 4.818429574)

Neither of these expressions is right. Starting with 8^(4x/3), how did you get 8^(16 8/15)? I'm assuming the part in parentheses is 16 + 8/15. If you substitute 12.4 for x, and multiply by 4/3, what do you get?

How did you get 4.8 x 10^14? That would be 480,000,000,000,000, nowhere close to 4.818...

Many thanks

 

[zebra1707]

Hi Mark

For this question - I need to substitute 12.4 into all x values.

(5x-3/x to the power 0) so if you substitute 12.4 into the x in this part of the equation (12.4^0), yes, you will get (5(12.4)/1).

Is a substitution question.

I don't yet understand how to add the Maths chararcters in the Forum.

Cheers

 

[Mark44]

Hi Mark

For this question - I need to substitute 12.4 into all x values.

That much is obvious.

(5x-3/x to the power 0) so if you substitute 12.4 into the x in this part of the equation (12.4^0), yes, you will get (5(12.4)/1).

No you don't. Where did the 3 go?

I still don't know what you mean when you wrote (5x-3/x^0), so please read what I wrote in my previous post more carefully and answer the questions that I asked.

Is a substitution question.

I don't yet understand how to add the Maths chararcters in the Forum.

Cheers

 

[zebra1707]

Really sorry,

If x = 12.4 Find the value of ... correct to two sig fgures

8^(4x/3) (divided by sign) log(base 10 subscript) (5x-3/x^0) - this is exactly how the question is written.

x to the 0 power is 1 so log(base10)(5x-3/1) = log 59

8 to the power of 4x/3 if you substitute 12.4 into x you get 8 to the power of 16 8/15

So. 8 to the power of 16 8/15 or (16.533333.) (divided by ) log(base10)(5x-3/1) = log 59.

Hope that helps - otherwise not sure how I can explain this further.

If I do this again I get 1.6 x 10^14
Cheers

 

[HallsofIvy]

Yes, it reduces to
$$\frac{8^{16.53333..}}{59}$$

but I do NOT get "1.6 x 10^14" for that.

 

[zebra1707]

Thanks HOI, I am getting two different answers and getting confused.

Ill have another look at this. Cheers

 

[Mark44]

This is a relatively straightforward problem in using a calculator. You shouldn't be getting two answers.

 

[zebra1707]

Thanks Mark, for all your help.

Cheers