Basic Exponential and Logarithmic Functions

[alexK2007]

(b) Find all x where x is an element of any real number : 4 (2^x + 2^-x) = 17
(c) Write 2 ln x + 1/2 ln (x^2 -1)-1/2 ln (x^2 +1) as a single logarithm.
(d) Find the exact value of 5^(2log5(3)+log5(2) )

 

[MarkFL]

Hello, and welcome to FMH!

I'll start on the first problem...let's distribute the 4 to get:

[MATH]4\cdot2^x+4\cdot2^{-x}=17[/MATH]
Now, what do you get if you multiply by \(2^x\)?

 

[alexK2007]

i'm not sure

 

[MarkFL]

i'm not sure

Give it a try...multiply every term on both sides of the equation by \(2^x\), recalling the exponent rule:

[MATH]a^b\cdot a^c=a^{b+c}[/MATH]