Evaluate the following exponential functions: f(x) = 2^3 when x = 3, f(x) = 5^(x+1) when x = 2, f(x) = e^x when x = 1, f(x) = 2^(x-1) when x = 2. Convert the logarithmic form into... Evaluate the following exponential functions: f(x) = 2^3 when x = 3, f(x) = 5^(x+1) when x = 2, f(x) = e^x when x = 1, f(x) = 2^(x-1) when x = 2. Convert the logarithmic form into its equivalent logarithmic form. Read more

Steps to Solve

1. Evaluate $f(x) = 2^3$ when $x = 3$

Substituting $x = 3$ into the function gives: $$ f(3) = 2^3 = 8 $$

2. Evaluate $f(x) = 5^{x+1}$ when $x = 2$

Substituting $x = 2$ into the function gives: $$ f(2) = 5^{2+1} = 5^3 = 125 $$

3. Evaluate $f(x) = e^x$ when $x = 1$

Substituting $x = 1$ into the function: $$ f(1) = e^1 = e $$

4. Evaluate $f(x) = 2^{x-1}$ when $x = 2$

Substituting $x = 2$ into the function gives: $$ f(2) = 2^{2-1} = 2^1 = 2 $$

5. Evaluate $f(x) = 4^{2-x}$ when $x = 2$

Substituting $x = 2$ into the function gives: $$ f(2) = 4^{2-2} = 4^0 = 1 $$

6. Convert the logarithmic expressions into equivalent forms

• For $2^3 = 8$, the logarithmic form is: $$ \log_2 8 = 3 $$

• For $3^1 = 3$, the logarithmic form is: $$ \log_3 3 = 1 $$

• For $4^2 = 16$, the logarithmic form is: $$ \log_4 16 = 2 $$