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 the exponential equation for x. {:[(5^(4x+3))/(25^(9-x))=5^(2x+5)],[x=]:}

Solve the exponential equation for x x .\newline54x+3259−x=52x+5x=□ \begin{array}{l} \frac{5^{4 x+3}}{25^{9-x}}=5^{2 x+5} \\ x=\square \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Compare linear, exponential, and quadratic growthright chevron icon

Full solution

Q. Solve the exponential equation for x x .\newline54x+3259−x=52x+5x=□ \begin{array}{l} \frac{5^{4 x+3}}{25^{9-x}}=5^{2 x+5} \\ x=\square \end{array}
  1. Recognize and simplify the equation: Simplify the equation by recognizing that 2525 is a power of 55.\newlineSince 25=52 25 = 5^2 , we can rewrite 259−x 25^{9-x} as (52)9−x (5^2)^{9-x} .\newlineThis gives us 54x+3/52(9−x)=52x+5 5^{4x+3} / 5^{2(9-x)} = 5^{2x+5} .
  2. Apply properties of exponents: Apply the properties of exponents to simplify the equation further.\newlineUsing the property am−n=am/an a^{m-n} = a^m / a^n , we can combine the exponents on the left side of the equation.\newlineThis gives us 54x+3−2(9−x)=52x+5 5^{4x+3 - 2(9-x)} = 5^{2x+5} .
  3. Simplify the exponent: Simplify the exponent on the left side of the equation.\newlineCalculate 4x+3−2(9−x) 4x+3 - 2(9-x) which simplifies to 4x+3−18+2x 4x+3 - 18 + 2x .\newlineThis simplifies further to 6x−15 6x - 15 .\newlineNow we have 56x−15=52x+5 5^{6x-15} = 5^{2x+5} .
  4. Set the exponents equal: Since the bases are the same and the equation is an equality, we can set the exponents equal to each other.\newlineThis gives us 6x−15=2x+5 6x - 15 = 2x + 5 .
  5. Solve the linear equation: Solve the linear equation for x.\newlineSubtract 2x 2x from both sides to get 4x−15=5 4x - 15 = 5 .\newlineThen add 15 15 to both sides to get 4x=20 4x = 20 .\newlineFinally, divide both sides by 4 4 to find x=5 x = 5 .

More problems from Compare linear, exponential, and quadratic growth

Question
Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits xx days to pick up the motorcycle.\newlineWrite an equation for the function. If it is linear, write it in the form g(x)=mx+bg(x) = mx + b. If it is exponential, write it in the form g(x)=a(b)xg(x) = a(b)^x.\newlineg(x)=‾g(x) = \underline{\hspace{3em}}
Get tutor helpright-arrow

Posted 1 month ago

Question
How does f(t)=−2t−7f(t)=-2t-7 change over the interval from t=−7t=-7 to t=−6t=-6?\newlineChoices:\newline[f(t) decreases by 2]\left[\text{f(t) decreases by } 2\right]\newline[f(t) increases by 2]\left[\text{f(t) increases by } 2\right]\newline[f(t) increases by 200%]\left[\text{f(t) increases by } 200\%\right]\newline[f(t) decreases by a factor of 2]\left[\text{f(t) decreases by a factor of } 2\right]
Get tutor helpright-arrow

Posted 1 month ago

Question
How does g(t)=9tg(t)=9^t change over the interval from t=1t=1 to t=3t=3?\newlineChoices: \newline[g(t) decreases by a factor of 81]\left[\text{g(t) decreases by a factor of } 81\right]\newline[g(t) increases by a factor of 81]\left[\text{g(t) increases by a factor of } 81\right]\newline[g(t) increases by 18%]\left[\text{g(t) increases by } 18\%\right]\newline[g(t) decreases by 9%]\left[\text{g(t) decreases by } 9\%\right]
Get tutor helpright-arrow

Posted 1 month ago

Question
Both of these functions grow as xx gets larger and larger. Which function eventually exceeds the other?\newline Choices:\newline(A)f(x)=8x+3.3(A)f(x) = 8x + 3.3\newline(B)g(x)=3.3x−5(B)g(x) = 3.3^x - 5
Get tutor helpright-arrow

Posted 2 months ago

Question
Both of these functions grow as x x gets larger and larger. Which function eventually exceeds the other?\newlineChoices:\newline(A) f(x)=2x+9(A) \ f(x) = 2x + 9 \newline(B) g(x)=2x(B)\ g(x) = 2^x
Get tutor helpright-arrow

Posted 2 months ago

Question
The functions f(x) f(x) and g(x) g(x) are differentiable. \newlineThe function h(x) h(x) is defined as: h(x)=g(x)f(x) h(x)=\frac{g(x)}{f(x)} \newlineIf f(8)=1 f(8)=1 , f′(8)=−6 f'(8)=-6 , g(8)=8 g(8)=8 , and g′(8)=−10 g'(8)=-10 , what is h′(8) h'(8) ? \newlineSimplify any fractions. \newlineh′(8)= h'(8)= ______
Get tutor helpright-arrow

Posted 2 months ago

Question
The functions p(x) p(x) and q(x) q(x) are differentiable. \newlineThe function r(x) r(x) is defined as: r(x)=p(x)q(x) r(x)= \frac{p(x)}{q(x)} \newlineIf p(3)=2 p(3)= 2 , p′(3)=4 p'(3)= 4 , q(3)=6 q(3)= 6 , and q′(3)=9 q'(3)= 9 , what is r′(3) r'(3) ? \newlineSimplify any fractions. \newliner′(3)= r'(3)= _____
Get tutor helpright-arrow

Posted 3 months ago

Question
The functions u(x) u(x) and v(x) v(x) are differentiable. \newlineThe function w(x) w(x) is defined as: w(x)=u(x)v(x) w(x)= \frac{u(x)}{v(x)} \newlineIf u(5)=3 u(5)= 3 , u′(5)=−2 u'(5)= -2 , v(5)=7 v(5)= 7 , and v′(5)=1 v'(5)= 1 , what is w′(5) w'(5) ? \newlineSimplify any fractions. \newlinew′(5)= w'(5)= _____
Get tutor helpright-arrow

Posted 3 months ago

Question
The functions a(x) a(x) and b(x) b(x) are differentiable. \newlineThe function c(x) c(x) is defined as: c(x)=a(x)b(x) c(x)= \frac{a(x)}{b(x)} \newlineIf a(2)=4 a(2)= 4 , a′(2)=5 a'(2)= 5 , b(2)=1 b(2)= 1 , and b′(2)=−3 b'(2)= -3 , what is c′(2) c'(2) ? \newlineSimplify any fractions. \newlinec′(2)= c'(2)= _____
Get tutor helpright-arrow

Posted 3 months ago

Question
The functions m(x) m(x) and n(x) n(x) are differentiable. \newlineThe function o(x) o(x) is defined as: o(x)=m(x)n(x) o(x)= \frac{m(x)}{n(x)} \newlineIf m(7)=2 m(7)= 2 , m′(7)=−1 m'(7)= -1 , n(7)=4 n(7)= 4 , and n′(7)=8 n'(7)= 8 , what is o′(7) o'(7) ? \newlineSimplify any fractions. \newlineo′(7)= o'(7)= _____
Get tutor helpright-arrow

Posted 3 months ago

View all (108)