Solve for x 8^(6+3x)=4

Problem

8(6+3*x)=4

Solution

1. Identify the common base for both sides of the equation, which is 2

2. Rewrite the numbers 8 and 4 as powers of 2

8=2

4=2

3. Substitute these powers back into the original equation.

(2)(6+3*x)=2

4. Apply the power of a power rule, which states (am)n=a(m⋅n) to the left side.

2(3*(6+3*x))=2

5. Distribute the 3 in the exponent.

2(18+9*x)=2

6. Equate the exponents since the bases are now the same.

18+9*x=2

7. Isolate the variable by subtracting 18 from both sides.

9*x=−16

8. Solve for x by dividing both sides by 9

x=−16/9

Final Answer

x=−16/9

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