Question

if 2^3x+1+2^7=2^8 then what is the value of 2^x​

Answer 1

Step-by-step explanation:

2^(3x-1)+10=7×6=42

=> 2^(3x-1) = 32

=> 2^(3x-1) = 2^5

As LHS IS HAVING SAME BASE AS THAT OF RHS therefore, we can now easily compare the powers

Therefore, => 3x-1 = 5

=> 3x = 6

=> X = 2

Hope u can get through the process…

Answer 2

Question

Solve for x, $2^{3x+1}+2^7=2^8$.

Solution

Exponential equations are solvable by comparing the powers. To solve this, we could isolate $x$ and the power. Let's get to the problem.

$2^{3x+1}+2^7=2^8$

$\rightarrow 2^{3x+1}=2^{8}-2^{7}$

$\rightarrow 2^{3x+1}=(2\times 2^{7})-2^{7}$

$\rightarrow 2^{3x+1}=2^{7}$

We take a log of base 2 because we need to compare the powers.

$\rightarrow 3x+1=7$

$\rightarrow \boxed{x=2}$

More information

• Why can exponential equations solved by comparing the powers?

→ $\boxed{f(a)=f(b) \iff a=b\ \mathrm{(If\:strictly\ increasing.)}}$

→ As $x$ goes up, $y$ goes up. In other words, this is because of the graph. We say a graph is 'strictly increasing or decreasing' when the graph doesn't give the same value once. And the exponential functions are strictly increasing.  We can say the values of power are the same if the values are the same.

→ To test this, draw a horizontal line on the graph. For the graph to be strictly increasing, it must go through one or no point.

→ The logic is used in factorial, exponential graph, $y=x^3$, inequality.