Master Logarithmic Equations: Expert Tips for Solving Problems

[bluff_boy]

Having problems with these questions, what's putting me off is for example the first question, if the numbers 9 and 5 were the same I think I could do it. Do I have to get them to the same number or do I just multiply them?

 

[micromass]

For (1). Take log of both sides and use logarithm rules.

That's about all the help I'm giving you right now. You make an effort now.

 

[eumyang]

For (ii), multiply both sides by e^t. Let w = e^t, and rewrite the equation in terms of w. What does the resulting equation look like now?

 

[Ray Vickson]

Having problems with these questions, what's putting me off is for example the first question, if the numbers 9 and 5 were the same I think I could do it. Do I have to get them to the same number or do I just multiply them?

(i) lhs= 125*[9^3 *5^2]^x = 125* 18225^x
rhs = 3^3*2^4/5^2 *[3^4/2/5^3]^x = (432/25)(81/250)^x.
Thus, [18225*250/81]^x = (432/25)/125.

(ii) Put x = exp(t) and see what you get.

(iii) Put x = ln(i+2). First you need to decide if $\ln(i+2)^6$ means $\ln [(i+2)^6]$ or $[ \ln (i+2) ]^6 .$

RGV