We read your photo as:

Solve the following equations: a) 2x3 = 16 b) 125^x = (1)/(5)

Mathematics

ScanSolve AI Answer

Answers

2 parts
a

x=2x = 2

b

x=−13x = -\frac{1}{3}

Step-by-step solution

6 steps

Here are the solutions to the equations:

Part a· 2 steps

Solve 2x3=162x^3 = 16

  1. Divide both sides by 2.

    2x32=162\frac{2x^3}{2} = \frac{16}{2} x3=8x^3 = 8

  2. Take the cube root of both sides.

    x=83x = \sqrt[3]{8} x=2x = 2

    The solution is x=2\boxed{x = 2}.

Part b

x=−13x = -\frac{1}{3}

Solve 125x=15125^x = \frac{1}{5}

  1. Express both sides with the same base.

    Note that 125=53125 = 5^3 and 15=5−1\frac{1}{5} = 5^{-1}.

    (53)x=5−1(5^3)^x = 5^{-1}

  2. Apply the exponent rule (am)n=amn(a^m)^n = a^{mn}.

    53x=5−15^{3x} = 5^{-1}

  3. Since the bases are the same, equate the exponents.

    3x=−13x = -1

  4. Divide by 3 to solve for xx.

    x=−13x = -\frac{1}{3}

    The solution is x=−13\boxed{x = -\frac{1}{3}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QSolve the following equations: b) 5^x - 6 imes 5^x+1 + 125 = 0. [Also, 3^x imes 5^x imes 7^x…QSolve the following exponential equations: a) 8^x = (1)/(4) b) 5^x+1 = 125 c) 32x−1 = (1)/(27) d)…QSolve for x in the following equations: a) 3x+2=0 b) 2x−4=0 c) x+1=0 d) 2^x+2=6 e) 3^x-3=6QSolve for x in the following equations: (i) (0.25)^x+1 = 16QSolve for x in the equations: 3.3.2 5^(x+2) = 1/25 and 3.3.1 27.3^x = 1
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp