Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

solve for xx 64x−9=(136)x−46^{4x-9}=(\frac{1}{36})^{x-4}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Solve equations with variable exponentsright chevron icon

Full solution

Q. solve for xx 64x−9=(136)x−46^{4x-9}=(\frac{1}{36})^{x-4}
  1. Identify base and exponent: Identify the base and the exponent on both sides of the equation.\newlineOn the left side, we have 64x−96^{4x-9}, and on the right side, we have (1/36)x−4(1/36)^{x-4}.
  2. Recognize 1/361/36 as 6−26^{-2}: Recognize that 1/361/36 can be written as 6−26^{-2}. So, (1/36)(x−4)(1/36)^{(x-4)} can be rewritten as (6−2)(x−4)(6^{-2})^{(x-4)}.
  3. Apply power of power rule: Apply the power of a power rule to the right side of the equation.\newlineAccording to the power of a power rule, (am)n=a(m∗n)(a^m)^n = a^{(m*n)}.\newlineSo, (6−2)(x−4)(6^{-2})^{(x-4)} becomes 6(−2∗(x−4))6^{(-2*(x-4))}.
  4. Distribute exponent: Distribute the exponent on the right side. 6(−2∗(x−4))6^{(-2*(x-4))} becomes 6(−2x+8)6^{(-2x+8)}.
  5. Set exponents equal: Set the exponents equal to each other since the bases are the same.\newlineWe now have 64x−9=6−2x+86^{4x-9} = 6^{-2x+8}.\newlineSo, 4x−9=−2x+84x - 9 = -2x + 8.
  6. Solve for x: Solve for x by combining like terms.\newlineAdd 2x2x to both sides to get 4x+2x=8+94x + 2x = 8 + 9.\newlineThis simplifies to 6x=176x = 17.
  7. Divide by 66: Divide both sides by 66 to solve for xx.x=176x = \frac{17}{6}.

More problems from Solve equations with variable exponents

Question
Write the expression using an exponent.\newline2×22 \times 2\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Evaluate the expression. 4−42 4 - 4^2 ____
Get tutor helpright-arrow

Posted 3 months ago

Question
x2=4x^2 = 4
Get tutor helpright-arrow

Posted 2 months ago

Question
x2=9x^2 = 9
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve for x. \newlinex2=0x^2 = 0 \newlineWrite your answer in simplified, rationalized form. \newlinex=x = _____ or x=x = _____
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve for xx. \newline8=2x8 = 2^x \newline x=x = _____
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve for xx. \newline6=7x6 = 7^x \newline x=x = _____
Get tutor helpright-arrow

Posted 4 months ago

Question
Select the equivalent expression.\newline((8−5)/(2−2))−4=?((8^{-5})/(2^{-2}))^{-4}=?\newlineChoose 11 answer:\newline(A) \newline(820)/(28)(8^{20})/(2^{8})\newline(B) \newline(26)/(89)(2^{6})/(8^{9})\newline(C) \newline(1)/(8⋅22)(1)/(8\cdot 2^{2})
Get tutor helpright-arrow

Posted 15 days ago

Question
Select the equivalent expression.\newline(b745)−3= ?\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?\newlineChoose 11 answer:\newline(A) b21415\frac{b^{21}}{4^{15}}\newline(B) 415b21\frac{4^{15}}{b^{21}}\newline(C) b−21⋅4−15b^{-21}\cdot 4^{-15}
Get tutor helpright-arrow

Posted 2 months ago

Question
Select the equivalent expression.\newline(33⋅66)−3=(3^{3}\cdot6^{6})^{-3}=?\newlineChoose 11 answer:\newline(A) 139⋅618\frac{1}{3^{9}\cdot6^{18}}\newline(B) 61839\frac{6^{18}}{3^{9}}\newline(C) 39618\frac{3^{9}}{6^{18}}
Get tutor helpright-arrow

Posted 2 months ago

View all (55)