which are possible first steps in solving the equation 4^x + 3 = 18? rewrite each side with base 2. subtract…

Explanation:

Step1: Analyze option 1

Since (4 = 2^2), rewriting (4^{x + 3}) as ((2^2)^{x+3}=2^{2(x + 3)}) and (18=2\times3^2) is a valid first - step to simplify the exponential equation using the property of exponents ((a^m)^n=a^{mn}).

Step2: Analyze option 2

Subtracting 18 from both sides gives (4^{x + 3}-18 = 0), which doesn't help in isolating the variable (x) in a useful way for an exponential equation.

Step3: Analyze option 3

Taking the base - 4 logarithm of both sides (\log_4(4^{x + 3})=\log_4(18)), by the property (\log_a(a^b)=b), we get (x + 3=\log_4(18)), which is a valid first - step to solve for (x).

Step4: Analyze option 4

Taking the natural logarithm of both sides (\ln(4^{x + 3})=\ln(18)), using the property (\ln(a^b)=b\ln(a)) gives ((x + 3)\ln(4)=\ln(18)), which is a valid first - step to solve for (x).

Step5: Analyze option 5

Taking the common logarithm of both sides (\log(4^{x + 3})=\log(18)), using the property (\log(a^b)=b\log(a)) gives ((x + 3)\log(4)=\log(18)), which is a valid first - step to solve for (x).

Answer:

A. Rewrite each side with base 2. C. Take the base - 4 logarithm of each side. D. Take the natural logarithm of each side. E. Take the common logarithm of each side.