SOLUTION: can someone help me with this question thanx. solve the following equation for x, giving the answer correct to two decimal places {{{5^(x-2)=2^(x+3)}}} this question is fro

Question 203500: can someone help me with this question
thanx.
solve the following equation for x, giving the answer correct to two decimal places

this question is from the book Longman Pre-U Text STPM Mathematics S & T Paper 1

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
To solve for x when it is in exponents is to use logarithms. Since we want our answer in decimal form (and not logarithm form) we need to use a logarithm we can get from out calculator (or other computing device). If calculators have any logarithms at all they will most likely have base 10 logarithms and/or natural (base e) logarithms. Either will work and give the correct answer to the problem.

Find the log of both sides:

Now we can get x out of the exponents by using the following property of logarithms (which applies to all bases): . Applying this to our logarithms we get:

We are now in a position to solve for x. We can either

replace the logarithms now with decimals and finish the solution with these decimals
Or, complete the solution with logarithms and replace them with decimals at the end.

I will use the second approach. But if you can't understand this, then repalce the logarithm's now and finish the solution using the decimals.
Subtract from both sides:

Add to both sides:

Divide both sides by :

We can get the logarithms above from our calculator:

Simplifying gives:

Rounded to 2 decimal places:

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