MHB Solve for x: 4^(x-5) = 7^(2x-1) | Equation Help

  • Thread starter Thread starter Nikolas7
  • Start date Start date
AI Thread Summary
To solve the equation 4^(x-5) = 7^(2x-1), logarithms can be applied to both sides, leading to (x-5)log 4 = (2x-1)log 7. This transformation utilizes the property of logarithms that states log(a^x) = x log(a). The equation can then be manipulated as a linear equation to find the value of x. The discussion concludes with the user confirming their understanding of the logarithmic property used in the solution.
Nikolas7
Messages
22
Reaction score
0
Help me with the following equation:
${4}^{x-5}$=${7}^{2x-1}$
 
Mathematics news on Phys.org
Nikolas7 said:
Help me with the following equation:
${4}^{x-5}$=${7}^{2x-1}$

you can take log on both sides and get $(x-5)\log\, 4 = (2x-1) log\, 7$ and because it is linear equation you can proceed to finish it
 
Please, show details how you got (x−5)log4=(2x−1)log7
 
Nikolas7 said:
Please, show details how you got (x−5)log4=(2x−1)log7

this is as per definition $\log\,a ^ x = x \log\, a $
 
Yes, I figured out, thanks
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Solve Equation: $x^4+2x^3-x^2-6x-3=0$
Replies
7
Views
1K
MHB -s6.6 solve exponential eq 3^x-14\cdot 3^{-x}=5
Replies
1
Views
1K
MHB 5.6.28 find domain of x in ABS
Replies
6
Views
1K
MHB Solving the Equation: x+[2x]+[3x]=7
Replies
4
Views
1K
MHB How can you solve $5^{x^2+8}=125^{2x}$ for x?
Replies
8
Views
1K
MHB Solve Floor Equation 7: x^2=2x-1
Replies
2
Views
1K
MHB Make x the subject of 2x/5-3b/4=x+5
Replies
5
Views
2K
MHB Solving the Floor Function Equation: $[x]=2x+1$
Replies
14
Views
2K
MHB Solve the Floor Value of x in $x^2+1=2x$
Replies
3
Views
1K
MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top