How to solve common log problem given the following with the help of calculator?

Question

the question is $$\log_{10}(x + 8) + 6 = 8$$

$$\log_{10}(x+8) = 2$$

$$10^2 = x + 8 $$

I just turned it into exponential form. Now my question is if i did this right at all? and if i did how would i go on solving it?

Answer 1

In solving equations involving exponentials and logarithms it's important to remember they are inverse operations of each other, so exponentiating both sides we get

$$\begin{align}\log_a x &= c \\ \Rightarrow a^{\log_a x} &= a^c \\ \Rightarrow x &= a^c\end{align}$$

or taking the logarithm of both sides we get

$$\begin{align}a^x &= c \\ \Rightarrow \log_a(a^x) &= \log_a c \\ \Rightarrow x\log_a(a) &= \log_a c \\ \Rightarrow x &= \log_a c\end{align}$$ by the laws of logarithms.