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:

Express the given expression without logs, in simplest form. Assume all variables represent positive values. (e^(ln(4w)+ln(10x^(3)))) Answer:

Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(eln⁡(4w)+ln⁡(10x3)) \left(e^{\ln (4 w)+\ln \left(10 x^{3}\right)}\right) \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Simplify radical expressions with variablesright chevron icon

Full solution

Q. Express the given expression without logs, in simplest form. Assume all variables represent positive values.\newline(eln⁡(4w)+ln⁡(10x3)) \left(e^{\ln (4 w)+\ln \left(10 x^{3}\right)}\right) \newlineAnswer:
  1. Apply Logarithm Property: Use the property of logarithms that ln⁡(a)+ln⁡(b)=ln⁡(ab)\ln(a) + \ln(b) = \ln(ab).eln⁡(4w)+ln⁡(10x3)e^{\ln(4w) + \ln(10x^{3})} can be rewritten using this property as eln⁡(4w⋅10x3)e^{\ln(4w \cdot 10x^{3})}.
  2. Simplify Inside Logarithm: Simplify the expression inside the logarithm. \newline4w×10x34w \times 10x^{3} simplifies to 40wx340wx^{3}.\newlineSo, eln⁡(4w)+ln⁡(10x3)e^{\ln(4w) + \ln(10x^{3})} becomes eln⁡(40wx3)e^{\ln(40wx^{3})}.
  3. Use Exponent Property: Use the property of logarithms and exponents that eln⁡(a)=ae^{\ln(a)} = a. Since the base of the natural logarithm (ln⁡\ln) is ee, we can simplify eln⁡(40wx3)e^{\ln(40wx^{3})} to just 40wx340wx^{3}.
  4. Check for Simplifications: Check for any possible simplifications or reductions. The expression 40wx340wx^{3} is already in its simplest form, assuming ww and xx are variables representing positive values.

More problems from Simplify radical expressions with variables

Question
f(x)=6x+52−14+5x f(x)=\frac{6 x+5}{2-\sqrt{14+5 x}} \newlineWe want to find lim⁡x→−2f(x) \lim _{x \rightarrow-2} f(x) .\newlineWhat happens when we use direct substitution?\newlineChoose 11 answer:\newline(A) The limit exists, and we found it!\newline(B) The limit doesn't exist (probably an asymptote).\newline(C) The result is indeterminate.
Get tutor helpright-arrow

Posted 9 months ago

Question
Let x4+y2=17 x^{4}+y^{2}=17 .\newlineWhat is the value of d2ydx2 \frac{d^{2} y}{d x^{2}} at the point (−2,1) (-2,1) ?\newlineGive an exact number.
Get tutor helpright-arrow

Posted 8 months ago

Question
What is the area of the region bound by the graphs of f(x)=x−2,g(x)=14−x f(x)=\sqrt{x-2}, g(x)=14-x , and x=2 x=2 ?\newlineChoose 11 answer:\newline(A) 196 \frac{19}{6} \newline(B) 992 \frac{99}{2} \newline(C) 1512 \frac{151}{2} \newline(D) 452 \frac{45}{2}
Get tutor helpright-arrow

Posted 7 months ago

Question
Let g(x)=x43 g(x)=x^{\frac{4}{3}} .\newlineg′(27)= g^{\prime}(27)=
Get tutor helpright-arrow

Posted 8 months ago

Question
Simplify ln⁡(1e) \ln \left(\frac{1}{\sqrt{e}}\right) \newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify ln⁡(1e) \ln \left(\frac{1}{e}\right) \newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
y=(sin⁡−1(5x2))3y=(\sin^{-1}(5x^{2}))^{3}
Get tutor helpright-arrow

Posted 8 months ago

Question
(10x3−5x2−6x)÷(2x2)\left(10x^{3}-5x^{2}-6x\right)\div\left(2x^{2}\right)
Get tutor helpright-arrow

Posted 8 months ago

Question
y=cos⁡4xsin⁡4xy=\cos^{4}x\sin^{4}x
Get tutor helpright-arrow

Posted 8 months ago

Question
35−310\frac{3}{5}-\frac{3}{10}
Get tutor helpright-arrow

Posted 8 months ago

View all (15)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant