Solve the following exponential equations

1) 10^2x + 27 =190

2) 4e^x-2 +5 =70

Question

Solve the following exponential equations

1) 10^2x + 27 =190

2) 4e^x-2 +5 =70

anonymous · Answer

You are solving for x right? Isolate x onto one side. Try to do that first and come back when you get stuck or confused about a step.

campbell_st · Answer

1. subtract 27 from both sides

$$10^{2x} = 163$$

take the base 10 log of both sides

use the fact

$$\log_{10}(10^{2x}) = 2x$$

then $$2x = \log _{10}163$$

$$x = \frac{\log _{10}(163)}{2}$$

campbell_st · Answer

Question 2

same process

do all the arithmetic 1st 

take the base e log to get an answer

anonymous · Answer

so, is the final answer of the seconed equation ganna be x= ln4 (65)/-2 ?!

campbell_st · Answer

$$4e^{x-2} = 65$$

then divide by 4

$$e^{x -2} = \frac{65}{4}$$

$$\ln(e^{x - 2}) = x-2$$

then $$x - 2 = \ln(\frac{65}{4})$$

$$x = 2 + \ln(\frac{65}{4})$$