Solving exponential equations with different bases

How do we solve exponential equations with different bases? Oh well, make the bases the same first! Sometimes it's easy, sometimes we might have to use a log property that b^logb(x)=x
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"Just Algebra" (by blackpenredpen) is dedicated to helping middle school, high school, and community college students who need to learn algebra. Topics include how to solve various equations (linear equations, quadratic equations, square root equations, rational equations, exponential equations, logarithmic equations, and more), factoring techniques, word problems, functions, graphs, Pythagorean Theorem, and more. We will also cover standardized test problems such as the SAT. Feel free to leave your questions in the comment!
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[skinnyladd]

for the second equation I did,
(2^4x) x 2 = 3^x
(16^x) x 2 = 3^x
(3^x)/(16^x) = 2
(3/16)^x = 2
Taking log base (3/16) on both sides
x = log base 3/16 (2)
x = -0.414 (which is the same as yours)

great problems, looking forward to more!

[l.w.paradis]

I like how this was explained so clearly and simply. Crisp, without needless complications.

[quantumnoctemus]

He teaches better in one second than many teachers in 1 hour.

[neilgerace]

"Surprising, right?"

Hahahaha

[real_u]

so that's when "log that's not base e" is important 😮

[LythMusic]

(3x+1)log2 = xlog4
3xlog2 + log2 = xlog4
3xlog2 - xlog4 = -log2
x(3log2-log4) = -log2
x = -log2/3log2-log4

[geopediashorts]

i just used the property of logarithms, where you put the exponent in front of the logarithm

[balduran]

It's cool how the answer to the second one still has 1, 2, 3, 4 in it.

[thomassidoti]

I love this guy. It's just funny because if he would have just took the ln of 2 and 3 in the first place he wouldn't have to re-write the answer

[TheNerdess]

Im supposed to solve using only natural log. that has been my problem finding examples of people solving with that and not log! Stuff like 2^(5x+4)=3^(3x-2) can you just write ln instead of log?