Question

Solve for x 5.2³x = 21.

Answer 1

D) 0.69

Explanation:

Given :

5 × 2³ˣ = 21

Divide by 5 on each side :

• 1/5 x 5 x 2³ˣ = 1/5 x 21
• 2³ˣ = 4.2

Taking the cubic root :

• ∛2³ˣ = ∛4.2
• 2ˣ = 1.61

Using logarithm values :

• log(2ˣ) = log(1.61)
• x log(2) = log(1.61)
• x = log (1.61) / log (2)
• x = log₂ (1.61)
• x = 0.69 (approximately)

Answer 2

D. 0.69

Explanation:

Given equation:

`5 \cdot 2^(3x)=21`

Divide both sides by 5:

`\implies (5 \cdot 2^(3x))/(5)=(21)/(5)`

`\implies2^(3x)=4.2`

`\textsf{Apply exponent rule} \quad a^(bc)=(a^b)^c:`

`\implies(2^3)^x=4.2`

`\implies8^x=4.2`

Take natural logs of both sides:

`\implies \ln 8^x=\ln 4.2`

`\textsf{Apply the log Power law} \quad \ln x^n=n\ln x :`

`\implies x \ln 8=\ln 4.2`

Divide both sides by ln 8:

`\implies (x \ln 8)/(\ln 8)=(\ln 4.2)/(\ln 8)`

`\implies x=(\ln 4.2)/(\ln 8)`

`\implies x=0.690129776...`

`\implies x=0.69 \: \sf (2\:dp)`