Log without a specific subscript is log base 10 Log base e is represented as ln (stands for natural log)

Taking natural log, we have, ln {3^x*5^24}=ln (5^ (2x)). But, ln (a*b)=lna*lnb, as also, lna^m=mlna. :. ln3^x+ln5^24=2xln5. :. xln3+24ln5=2xln5. :. 24ln5=2xln5-xln3=x (2ln5-ln3). rArr x= (24ln5)/ (2ln5-ln3).

2018年1月16日 · But we have an #x# as the base! So we must use a special technique which involves talking the natural log # (ln)# of both sides and using implicit differentiation

#1/20 = (1/2)^ (t/ (3.8" days"))# Use the natural logarithm on both sides: #ln (1/20) = ln ( (1/2)^ (t/ (3.8" days")))# Use the identity, #log_b (a^c) = (c)log_b (a)#, on the right side of the equation: #ln (1/20) = (t/ …

2016年7月7日 · Using the properties of the logarithm we find that x~=4.91 To solve this equation we need to perform the "anit-log" of the equation, which is the exponential function or e^x where …

So, the first result is v=225e^ (-3)= 11.2 V For the second question, we take the natural log of the equation, using 115 V for v: ln (115) = ln (225)+ ln (e^ (- (Rt)/L)) Since ln and e are inverse operations, …

Explanation: Given: #int dy/ (4y) = int dx/ (1+x)# Multiply both sides by 4: #int dy/ (y) = 4int dx/ (1+x)# Integrate: #ln|y|=4ln|x+1|+C# Move the 4 inside as a power: #ln|y|= ln ( (x+1)^4)+C# Make both sides …

2018年6月12日 · Explanation: Let #y= (x^x)^x = x^ (x^2)# Then #log y = x^2 log x implies# #1/y dy/dx = 2x log x+x^2times 1/x= x (2 log x+1)# #dy/dx = x (2 log x+1) (x^x)^x# Answer link Guillaume L. · …

What is the derivative of #ln ( secx+tanx)#? How do you determine whether the function #f (x) = x/ (x^2 - 5)# is concave up or concave down and its intervals? How do you use the Intermediate Value …

Here, by the Change of Base Rule, #log_10I=lnI/ln10#