Solve for x:

10^(6x+6)=5

Question

Solve for x:

10^(6x+6)=5

amistre64 · Answer

i dunno, x looks pretty comfy there, im afraid to disturb it and have it all grumpy

anonymous · Answer

To bring variable expressions out of the exponents use a log. (log base 10 is a nice one for this since the base of the power is 10 here and log base 10 can be done with a calculator)

amistre64 · Answer

i was thinking to use the log10 meself, dont want to rock the boat and wake that sleeping giant tho

anonymous · Answer

How do I use log to bring the variable out of the exponent?

amistre64 · Answer

$$B^x=N$$
$$log_B(B^x)=log_B(N)$$
$$x=log_B(N)$$ is the results

amistre64 · Answer

or how to get to the results; logs undo exponents; and exponents undo logs;  they are inverses

amistre64 · Answer

$$10^{(6x+6)}=5$$
$$log_{10}10^{(6x+6)}=log_{10}5$$
$$6x+6=log_{10}5$$
$$6x=log_{10}(5)-6$$
$$x=\frac{log_{10}(5)}{6}-\frac{6}{6}$$

anonymous · Answer

Ok, makes sense to me. Thanks.

amistre64 · Answer

the log <-> exp relation is just like the * <->/ and the + <-> - relations; they undo each other when the time comes