Solve the exponential equation.

01 / Standard#Your turn

6^x-2^x=2^{x+1}-6^{x+1}+2^{x+2}

Official paper · jm01-2022 · I.14 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Factor shifted powers into constants times 6ˣ and 2ˣ.

Hint 2

Divide by the positive factor 2ˣ.

Worked solution

Collect the two exponential bases.
$6^x-2^x=6\cdot2^x-6\cdot6^x\implies7\cdot6^x=7\cdot2^x$
Use injectivity of the exponential.
$3^x=1\implies x=0$

C: x=0.

Checks and common pitfalls: 6ˣ⁺¹ is 6·6ˣ, not 6ˣ+1.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Collect the two exponential bases.
$6^x-2^x=6\cdot2^x-6\cdot6^x\implies7\cdot6^x=7\cdot2^x$
Use injectivity of the exponential.
$3^x=1\implies x=0$

Think first. Reveal a hint when the class is ready.

2022 JM01