Questions: Without using a calculator, solve the following equation. 5^x=26 Choose the correct answer below. A. x=ln 26/ln 5 B. x=26 ln 5 C. xx=ln 5/ln 26 D. x=5 ln 26

Without using a calculator, solve the following equation.
5^x=26

Choose the correct answer below.
A. x=ln 26/ln 5
B. x=26 ln 5
C. xx=ln 5/ln 26
D. x=5 ln 26

Transcript text: Without using a calculator, solve the following equation. \[ 5^{x}=26 \] Choose the correct answer below. A. $x=\frac{\ln 26}{\ln 5}$ B. $x=26 \ln 5$ C. $x_{x}=\frac{\ln 5}{\ln 26}$ D. $x=5 \ln 26$

Solution

Solution Steps

Step 1: Isolate the exponential term

Given the equation of the form $a^{bx} = c$, we start by taking the logarithm of both sides to isolate the exponent. This gives us $bx \log(a) = \log(c)$.

Step 2: Solve for $x$

Next, we solve for $x$ by dividing both sides by $b\log(a)$, which yields $x = \frac{\log(c)}{b\log(a)}$.